Place an oven rack in the upper third of the oven and preheat the oven to its highest setting, ideally 500°F (260°C).

Combine 1 1/4 cups warm water, 2 1/4 teaspoons active dry yeast, and 1 teaspoon sugar in the large mixing bowl.

Let the yeast mixture stand until foamy, about 5 to 10 minutes.

Add 3 cups flour and 1 teaspoon salt to the activated yeast mixture.

Stir in 1 tablespoon olive oil until a shaggy dough forms.

Transfer the dough to a lightly floured work surface and knead until smooth and elastic, about 8 to 10 minutes.

Form the dough into a ball and return it to the lightly oiled mixing bowl.

Cover the bowl with a clean kitchen towel and let the dough rise in a warm place until doubled, about 60 to 90 minutes.

Punch down the risen dough and divide it into 2 equal dough balls.

Dust the work surface with flour and stretch or roll 1 dough ball into a thin 10- to 12-inch round.

Spread about 1/4 cup pizza sauce evenly over the dough, leaving a small border around the edge.

Top the pizza with half the provolone cheese and half the Parmigiano Reggiano.

Bake the pizza until the crust is browned in dark spots and the cheese is bubbling, about 8 to 12 minutes.

Scatter half the fresh basil leaves over the hot pizza and slice it into portions.

Repeat the shaping, topping, baking, and finishing process with the remaining dough ball and toppings.