Add 2 1/2 cups warm water to a large bowl then whisk in the yeast and sugar. Let the mixture sit until foamy, 5 to 10 minutes.
Using a rubber spatula, stir in the flour, salt, 1 teaspoon pepper and 1/2 cup Parmesan cheese until the dough is cohesive.
Add 4 tablespoons olive oil to a large bowl. Transfer the dough to the bowl and turn it so that it’s coated in the oil. Cover the bowl with plastic wrap and leave it at room temperature to rise until it has doubled in size, about 2 hours. (See Kelly’s Note.)
Add 2 tablespoons olive oil to a 13x9-inch baking pan, brushing it to coat the bottom and sides.
Gently gather the edges of the dough on two sides and lift them up toward the center of the bowl. Give the bowl a quarter turn then repeat the folding over process to gently deflate the dough and shape it into a rough ball.
Transfer the dough into the prepared baking pan then pour any remaining oil from the bowl on top of the dough. Let the dough rise in a warm spot, uncovered, until it has doubled in size, about 1 hour.
Preheat the oven to 450°F.
Lightly coat your hands with olive oil then indent your fingers across the top of the dough to form dimples. Drizzle the dough with an additional 1 tablespoon olive oil then sprinkle it with the remaining 1/4 cup Parmesan cheese and 1/4 teaspoon black pepper.
Bake the focaccia until it is golden brown in color, 20 to 30 minutes. Remove it from the oven and serve.