Process flour, yeast, and salt in food processor until combined, about 2 seconds. With processor running, slowly add oil, then water, and process until dough forms sticky ball that clears sides of bowl, 1-½ to 2 minutes. If dough is sticky and clings to blade, add extra flour, 1 tablespoon at a time, as needed until it clears sides of bowl)

Transfer dough to lightly floured counter and shape into tight ball. Place dough in large, lightly oiled bowl and cover tightly with plastic wrap and towel. Let rise at room temperature until doubled in size, 1 to 1-½ hour.

Adjust rack to upper-middle position and heat oven to 500 degrees.

Pulse tomatoes, garlic, salt and 1 tablespoon oil together in good processor until coarsely ground, about 12 pulses. Transfer mixture to liquid measuring cup and add reserved tomato juice until sauce measures ¾ cup.

Place dough on lightly floured counter. Press and roll dough into 11-inch round. Grease 12-inch ovensafe skillet with 2 tablespoons oil. Transfer dough to skillet; reshape as needed. Spread sauce over dough, leaving about ½-inch border at the edge. Sprinkle mozzarella and Parmesan evenly over sauce. Add toppings of your choice and another layer of cheese.

Set skillet over high heat and cook until outside edge of dough is set, pizza is slightly puffed, and bottom crust is spotty brown when gently lifted with spatula, about 3 minutes.

Transfer pizza to oven and bake until crust is brown and cheese is golden in spots. 7 to 10 minutes. Using potholders, remove skillet from oven and slide pizza onto cutting board. Let pizza cool for 5 minutes before slicing and serving.