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1
Heat olive oil in a medium saucepan over medium heat until shimmering. Add garlic, oregano, and pepper flakes and cook, stirring constantly, until fragrant, about 1 minute. Add tomatoes. Increase heat to high, bring to a boil, then reduce to a bare simmer. Cook, stirring occasionally, until reduced by 1/4, about 20 minutes. Add heavy cream, increase heat to bring to a boil, reduce to a simmer, and continue to cook until reduced again by 1/4, about 20 minutes longer. Add vodka and cook for 7 minutes. Remove from heat and season to taste with salt and pepper.
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2
Let sauce cool slightly, then transfer half of sauce to the jar of a blender. Blend, starting on lowest speed and gradually increasing to high until completely smooth, about 2 minutes total. Strain through a fine mesh strainer into a medium bowl. Repeat with remaining half of sauce. Sauce can be stored in a sealed container in the refrigerator for up to 1 week (see note).
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3
At least 45 minutes before baking, place a baking stone or steel on an oven rack set to the top position and preheat oven to 550u00b0F.
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4
Turn single dough ball out onto lightly flour surface. Gently press out dough into rough 8-inch circle, leaving outer 1-inch higher than the rest. Gently stretch dough by draping over knuckles into a 12 to 14-inch circle about 1/4-inch thick. Transfer to pizza peel.
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5
Spread approximately 3/4 cup of sauce evenly over surface of crust, leaving 1/2 to 1-inch border along edge. Place 8 to 10 chunks of mozzarella evenly over surface of pizza and scatter with 4 to 5 basil leaves. Drizzle with about 1 tablespoon extra-virgin olive oil and sprinkle with with salt. Slide pizza onto stone or steel and bake until cheese is melted and crust underbelly is spotty brown, 6 to 12 minutes total. Remove from oven with metal pizza peel, transfer to cutting board, slice, and serve. Repeat steps 3 and 4 with remaining ingredients to make 2 additional pizzas.
