Using a stand mixer fitted with a dough hook, mix the all-purpose flour, semolina flour, sugar, and yeast on low speed until combined. With the machine running, slowly add the water and oil until a dough forms and no dry flour remains 1 to 2 minutes. Cover with plastic wrap and let the dough rest for 10 minutes.

Add the salt to the dough and mix on medium speed until the dough forms a smooth, sticky ball that clears the sides of the bowl, 6 to 8 minutes. Remove the dough from the bowl and knead briefly on a lightly floured counter until smooth, about 1 minute. Shape the dough into a tight ball and place in a large, lightly oiled bowl. Cover tightly with plastic wrap and refrigerate for at least 24 hours or up to 48 hours.

Make the Sauce: Heat the oil and garlic in a medium saucepan over medium-low heat, occasionally stirring, until the garlic is fragrant and just beginning to brown, about 2 minutes. Add the tomato paste, oregano, and red pepper flakes and cook until fragrant, about 30 seconds. Add the crushed tomatoes, sugar, and salt and cook, occasionally stirring, until the sauce measures 2 cups, 25 to 30 minutes. Transfer to a bowl, allow to cool and refrigerate until needed.

Place a baking stone on the upper-middle rack and preheat oven to 500 degrees F. Spray a rimmed baking sheet with non-stick cooking spray, then coat the bottom of the pan with the olive oil.

Remove the dough from the refrigerator and transfer it to a lightly floured surface. Lightly flour the top of the dough and gently press into a 12x9-inch rectangle. Using a rolling pin, roll the dough into an 18x13-inch rectangle. Transfer the dough to the prepared baking sheet, fitting the dough into the corners. Spray the top of the dough with non-stick cooking spray and lay a sheet of plastic wrap over the dough. Place a second baking sheet on the dough and let it stand for 1 hour.

Remove the top baking sheet and plastic wrap. Gently stretch and light dough to fill the pan. Spread the sauce in an even layer over the surface of the dough, leaving a ½-inch border. Sprinkle the Parmesan evenly over the entire surface of the dough, then repeat with the mozzarella cheese.

Place the pan on the baking stone, reduce the oven temperature to 450 degrees F and bake until the cheese is bubbly and browned, 20 to 25 minutes, rotating the pan halfway through baking. Remove the pan from the oven and cool on a wire rack for 5 minutes. Run a knife around the rim of the pan to loosen the pizza. Transfer to a cutting board, cut into squares, and serve.