I was sitting next to a forklift inside a brewery in Queens when I understood that everything I knew about New York pizza was wrong. Until that moment, I would have told you that the best pizza in the city comes out of a large oven that is either built into a wall or weighs so much that it might as well be; that the dough needs to be soft, stretchy and raw when it begins to bake; and that the toppings should be somewhat Italian – if not in tradition, then at least in spirit. There I was, though, eating a 10-by-10-inch pie with a parbaked crust. This was topped with crumbled Egyptian fava bean falafel squirted with halal-cart white sauce. Then it went into a countertop electric oven smaller than the average microwave. And I enjoyed every heretical square inch. The person responsible for this epiphany was Natalie DeSabato, who sells square pies with a grandma-style crust at bars, breweries and other spots around the city under the name Traze. She is one of several nomadic cooks who set up inexpensive, compact, portable ovens in locations that would otherwise have no pizza at all. Since the start of this decade, on-the-fly food businesses of all sorts have sprung up in the city, cultivating a following through pop-ups and product drops announced on social media without the expense or stability of a permanent address. Some of the busiest have been these mobile pizza kitchens. In a sense, pop-up pizzerias are a byproduct of new technology. The ovens they use, including the electric Breville Pizzaiolo and several models made by Ooni that run on propane or wood pellets, were designed for home use and introduced during the past decade. These devices have allowed a batch of self-taught pizza makers to storm a tradition-bound business that hasn’t always been easy for outsiders to break into. Two of the most avidly followed pop-ups in the city are run by women, which is still unusual at brick-and-mortar pizzerias. Some of these bakers emulate traditional pizza styles, scaled down to the 12-inch diameters their ovens can hold. Others wing it with ideas of their own. Most do both. I met Auggie Russo and his pies on a warm night last fall when he was running his Tiny Pizza Kitchen pop-up in the backyard of a bar in Clinton Hill, Brooklyn. He was tending a propane-fueled Ooni Koda oven that, with its flat floor and low, sloping roof, looked like the scoop on the hood of a 1969 Plymouth Road Runner. The temperature inside the device was above 900 degrees, almost as hot as the classic wood-burning pizza ovens of Naples, and one of Russo’s three pies that evening was a by-the-book margherita. It had the black bubbles, crisp rim and airy interior that Neapolitan pizza groupies line up for. The other two were pure Tiny Pizza Kitchen originals. One, the Miss Betty White, is Russo’s name for a seasonal vegetable pizza. Each time Miss Betty White appears, her wardrobe changes, depending on what Russo has found in the produce markets lately. On that night, she was dressed in gooseberries, pomegranate seeds, spiced butternut squash and sautéed leeks, among other things, and accessorized with edible flowers and fresh herbs. The other pizza, A Farewell to Figs, featured raw figs Russo had picked from a backyard tree belonging to some generous friends; spicy fig jam from a small-batch preserves outfit in California; charred cherry tomatoes; salted raw onions; thin ribbons of salami; and at least five kinds of cheese. Remarkably, all the ingredients stayed in harmony, although they didn’t all necessarily stay on top of the pizza. Miriam Weiskind, who calls her floating pizzeria the Za Report, lets the dough for her round, 12-inch pies ferment for four days, during which the yeast breaks the starches down into compounds that give the crust a smooth, well-rounded taste and a texture more soft than crisp. At some of her pop-ups, she serves only thick, cushiony Sicilian squares; that dough goes through a seven-day process and comes out with a graceful, light-footed texture unusual for Sicilian pizza. The last Za Report pizza I ate, during a pop-up at Wild East Brewing in Brooklyn, was a round pie baked under a thin layer of hickory-smoked mozzarella, topped with soft red onions and dried cherries. Little ricotta rosettes, blooped out of a pastry tube, filled in the empty spaces. Luxardo cherry liqueur had been stirred into the ricotta, turning it pink and slightly sweet. On my way out, I told Weiskind that cherry pizza was somehow exactly what I’d been in the mood to eat. “I’m glad that I was able to fulfill your pizza dreams this evening,” she said. Single pies at these pop-ups start at around $15 and can go up to $25 or so. When I think about the energy it takes to lug multiple ovens; bins of wet dough and sauce; and multiple toppings, some of them cooked in advance, the prices don’t seem excessive at all. Although pop-up pizza is a national phenomenon, the New York school reflects local tastes. Felix Toro, whose Happy Bull Pizza is one of the most heavily booked pop-ups in town, makes pizzas with New York flavors on top of a crisp crust that, with its heavy char and exuberant blisters, suggests New Haven. In pursuit of pizza know-how, he took lessons from Anthony Falco, formerly of Roberta’s in Bushwick, and worked at Paulie Gee’s in Greenpoint and King Umberto in the Nassau County hamlet of Elmont. Using a Breville oven, Toro makes an extroverted pepperoni pizza with fresh jalapeños and hot honey. His juicy, garlic-drenched vodka pies are superb. Oregano and garlic powder sprinkled over the sauce give all his pizzas what he calls “my little oomph that makes it New York.” The crunchiest crust I’ve eaten on a pop-up pizza was achieved by Josiah Bartlett, whose business is called Wizard Hat Pizza. Bartlett bakes his pies in 615-degree heat inside a double-decker electric countertop oven manufactured in Turkey. Because it’s larger and heavier than the Pizzaiolo, he tends to leave it plugged in at one location for long periods of time. Until last Thursday, it lived and baked for two years in the basement of a low-key, vinyl-record-loving Brooklyn bar called Any Thing. In June, Wizard Hat will start a new residency in the dormant retail space of Chickadee Bread, a bakery in Prospect-Lefferts Gardens. Tracking down other pop-ups requires frequent checks of their Instagram accounts or the food recommendation app 8it, which can sort them by their distance from your phone. Happy Bull turns up from time to time at Boris & Horton, a dog-friendly cafe in the East Village. Traze has appeared at small rock clubs where DeSabato’s band, Ratas en Zelo, was playing, but her Brevilles have a tendency to overload the circuit breakers. In general, the easiest place to spot one of these pizzerias is in a brewery. Fifth Hammer, Grimm Ales, Finback, Evil Twin, Wild East and a few other spaces where beer is made and drunk are to pop-up pizza what the Central Park Ramble is to warblers. Naturally, the more popular a pop-up gets, the more likely its baker is to think about settling down. Weiskind hopes to open a place of her own next year; she will do fewer events this spring and summer while she works in a Chicago pizzeria to study how sit-down restaurants work. Russo has been looking for a permanent space, too. I asked him whether the routine of making pizza in the same place every night might not put him in a creative rut. He said he thought he’d have more time to invent and started talking about the membrillo he made during quince season and was thinking of putting on a roast-duck pizza. I’d go to his restaurant to eat that, but it would leave a hole in the pop-up landscape. Whenever I start to worry about how empty the breweries will be if all the pizza makers graduate to the next level, I comfort myself by thinking about all the Oonis and Brevilles in apartments and backyards around the city. At least one of them has to be owned by somebody who has a great dough recipe and wants to take it out on the road.