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1
Make the dough: Combine the yeast, 1 cup warm water (about 100 degrees F) and the sugar in a food processor and pulse once to combine.
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2
Let sit until foamy, 5 to 10 minutes.
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3
Add the olive oil and pulse to combine.
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4
Mix the flour and 2 teaspoons salt in a medium bowl; add to the food processor and pulse until the dough pulls away from the side and gathers around the blade.
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5
Turn the dough out onto a lightly floured surface and form into 2 even balls.
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6
Transfer to 2 lightly oiled bowls; cover with plastic wrap and let rise in a warm place until doubled in size, 2 to 4 hours.
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7
(You can make the dough ahead; wrap in plastic and refrigerate up to 1 week or freeze up to 2 months.
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8
Bring to room temperature before using.)
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9
Set a pizza stone or large baking sheet on the lowest oven rack and preheat to 500 degrees F. Meanwhile, make the topping: Combine the tomatoes, olive oil, garlic, red pepper flakes and 1 teaspoon salt in a bowl.
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10
Stretch 1 ball of dough into a 12-inch round on a lightly floured pizza peel or inverted baking sheet.
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11
Spread about 1/2 cup of the tomato mixture on the dough, leaving a 1/2-inch border.
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12
Top with half of the mozzarella, then brush the edge lightly with olive oil.
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13
Slide the pizza onto the hot stone or baking sheet and bake until the crust is golden and the cheese is bubbling, 8 to 10 minutes.
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14
Transfer to a cutting board and let cool 2 minutes before slicing.
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15
Repeat to make the second pizza.