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. Let sit until foamy, 5 to 10 minutes. Add the olive oil and pulse to combine. 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.
Turn the dough out onto a lightly floured surface and form into 2 even balls. 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. (You can make the dough ahead; wrap in plastic and refrigerate up to 1 week or freeze up to 2 months. Bring to room temperature before using.)
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.
Stretch 1 ball of dough into a 12-inch round on a lightly floured pizza peel or inverted baking sheet. Spread about 1/2 cup of the tomato mixture on the dough, leaving a 1/2-inch border. Top with half of the mozzarella, then brush the edge lightly with olive oil.
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. Transfer to a cutting board and let cool 2 minutes before slicing. Repeat to make the second pizza.
Recipe courtesy of Food Network Magazine