After mixing in step 1, the dough will be very sticky. Be sure to coat your hands with flour before transferring the dough from the mixing bowl to the greased bowl.
Dough
1/2 cup extra-virgin olive oil
1 3/4 cups water, heated to 110 degrees
1 tablespoon sugar
5 cups all-purpose flour
2 envelopes instant or rapid-rise yeast (4 1/2 teaspoons)
2 teaspoons salt
Sauce and Toppings
2 tablespoons extra virgin olive oil
3 garlic cloves , minced
1 1/2 teaspoons dried oregano
1/4 teaspoon red pepper flakes
2 tablespoons tomato paste
1 (28-ounce) can crushed tomatoes
2 tablespoons chopped fresh basil
Salt
1 1/2 cups grated Parmesan cheese
3 cups shredded mozzarella cheese
For the dough: Adjust oven rack to lowest position and heat oven to 200 degrees. When oven reaches 200 degrees, turn off oven. Grease large bowl. Evenly coat 18- by 13-inch rimmed baking sheet with 1/4 cup oil.
Combine water, sugar, and remaining oil in measuring cup. In bowl of standing mixer fitted with dough hook, mix flour, yeast, and salt on low speed until combined. Increase speed to medium-low and slowly add water mixture until dough is uniform in texture, about 3 minutes. Transfer dough to prepared bowl, cover with plastic, and place in warm oven. Let rise until doubled in size, about 30 minutes.
For the sauce and toppings: Heat 1 tablespoon oil in large saucepan over medium heat until shimmering. Cook garlic, oregano, and pepper flakes until fragrant, about 30 seconds. Stir in tomato paste and cook until just beginning to brown, about 2 minutes. Add tomatoes and simmer until reduced to 3 cups, about 10 minutes. Off heat, stir in basil and season with salt.
On lightly floured work surface, use rolling pin to roll dough into 16- by 12-inch rectangle. Transfer dough to prepared baking sheet and stretch dough to cover pan, pressing dough into corners. Brush dough with remaining oil and cover with plastic wrap. Set in warm spot (not oven) until slightly risen, about 20 minutes. Heat oven to 450 degrees.
Remove plastic wrap and, using fingers, make indentations all over dough. Sprinkle dough with 1 cup Parmesan and bake until cheese begins to melt, 7 to 10 minutes. Remove baking sheet from oven and spoon sauce over pizza, leaving 1-inch border. Bake until sauce is deep red and steaming, 7 to 10 minutes.
Sprinkle mozzarella and remaining Parmesan evenly over sauce and bake until cheese is golden brown, about 12 minutes. Remove pizza from oven and let rest 5 minutes. Serve.