Using a wooden spoon or spatula, stir flour, salt, and yeast together in a bowl.

Add warm water and mix until most of the flour is moistened.

Using your hands, knead dough in the bowl until it forms a sticky ball, about 1 minute.

Spray a 9-inch pie plate or cake pan with oil spray.

Transfer dough to the prepared plate and press into a 7- to 8-inch disk.

Spray the top of the dough with oil spray, cover tightly with plastic wrap, and refrigerate for 12 to 24 hours.

For the sauce, place tomatoes in a fine-mesh strainer and crush with your hands. Drain well, then transfer to a food processor.

Add oil, garlic, sugar, salt, oregano, and pepper flakes and process until smooth, about 30 seconds.

Two hours before baking, remove dough from the refrigerator and let sit at room temperature for 30 minutes.

Coat the bottom of a 12-inch cast-iron skillet with oil.

Transfer dough to the prepared skillet and use your fingertips to flatten dough until it is ⅛ inch from the edge of the skillet.

Cover tightly with plastic and let rest until slightly puffy, about 1½ hours.

Thirty minutes before baking, adjust oven rack to the lowest position and heat oven to 400 degrees.

Spread ½ cup sauce evenly over the top of the dough, leaving a ½-inch border (save remaining sauce for another use).

Sprinkle Monterey Jack evenly over the border and press it into the side of the skillet, forming a ½- to ¾-inch-tall wall.

Evenly sprinkle mozzarella over the sauce.

Bake until cheese at the edge of the skillet is well browned, 25 to 30 minutes.

Transfer skillet to stovetop and let sit until sizzling stops, about 3 minutes.

Run a butter knife around the rim of the skillet to loosen pizza.

Using a thin metal spatula, gently lift the edge of the pizza and peek at the underside to assess browning.

Cook pizza over medium heat until the bottom crust is well browned, 2 to 5 minutes.

Using 2 spatulas, transfer pizza to a wire rack and let cool for 10 minutes. Slice and serve.