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To prepare the dough: Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. In a large bowl or the bowl of a stand mixer fitted with the flat beater attachment, combine the flour, water, yeast, olive oil, and salt. Mix until a shaggy, sticky dough forms without any dry, floury patches. This should take less than 1 minute. Scrape down the sides to gather the dough into a rough ball. Cover and set aside.
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After 30 minutes, use a bowl scraper or your wet hand to grab a section of dough from one side, lift it up, and press it down to the center to seal. Repeat, turning the bowl 90° (a quarter-turn) between each stretch, until the dough won’t elongate easily, about 8 to 12 times total. This process, which is called a bowl fold, replaces kneading.
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Cover the bowl and let the dough rest at room temperature, undisturbed, for at least 30 minutes or for up to 3 hours. This forgiving dough will be fine with more or less time, but a longer rise will make shaping easier.
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Turn the dough out onto a lightly floured work surface. Gently deflate it and divide it in half (about 270g per piece).
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Shape each piece of dough into a rough ball by pulling the edges into the center. Turn the dough seam-side down, cover, and let rest for at least 20 minutes and up to 1 hour, until it’s relaxed enough to stretch. While the dough is resting, make the parsley oil.
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To make the parsley oil: In a small bowl, combine the olive oil, parsley, lemon juice, and garlic. Stir to combine and season with red pepper flakes and salt to taste. Set aside.
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To prepare your oven: Preheat the oven to 550°F (or 500°F if your oven doesn't get that hot) with a baking steel or stone inside on the middle rack. You need at least 8" clearance between your pizza and the broiler — otherwise, the pizza will burn before the bottom has had time to bake through. (A bottom-drawer broiler will not work here; see “tips” below for more information and alternative instructions.) Make sure your oven is at the required temperature for at least 30 minutes before baking so that the steel or stone can fully preheat.
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To shape the pizzas: Transfer one ball of dough to a sheet of parchment dusted with semolina or cornmeal. Sprinkle the top with flour. Use your fingertips to gently depress the round, stretching and pulling the dough gently into a 10" circle. Take care to leave a thicker rim around the circumference for a beautiful bubbly outer crust.
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Move your shaped dough to a pizza peel, a thin wooden cutting board, a rimless baking sheet, or an inverted baking sheet. Trim the excess parchment around the dough to prevent it from burning.
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To top the pizza: Lightly brush the center of the pizza with parsley oil, avoiding the outer rim. Evenly pour 1/4 cup (67g) of the vegan mozzarella in the center of the dough, then use a small offset spatula or the back of a spoon to spread it evenly to the edges. Sprinkle about half of the “chorizo” (64g) over the mozzarella, then evenly distribute a couple of small spoonfuls of parsley oil over top.
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Turn on the top broiler in your preheated oven and transfer the topped pie to your preheated steel or stone (here’s how!). Broil the pizza for approximately 6 minutes on the steel or 7 minutes on the stone (give or take), until crust is firm and charred in spots and cheese is bubbling. Watch carefully as ovens may vary.
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While your first pizza bakes, brush the second pizza with a light layer of parsley oil and top with the remaining vegan mozzarella and “chorizo.” Add a few spoonfuls of parsley oil on top, and repeat the baking process for the second pizza.
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Drizzle pizzas with any additional parsley oil when they come out of the oven. Carefully cut hot pizzas into slices and serve as soon as the pizza is cool enough to handle.
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Storage information: Store any leftover slices of vegan pizza in the refrigerator for several days. Reheat in a low oven (350°F) for several minutes until warmed through.