In a large bowl, combine the water, yeast, and sugar and stir to combine. Let sit until the mixture is foamy, about 5 minutes.
Add 1 1/2 cups of the flour, the semolina, 1/2 cup of the oil, and the salt, mixing by hand until it is all incorporated and the mixture is smooth. Continue adding the flour, 1/4 cup at a time, working the dough after each addition, until all the flour is incorporated but the dough is still slightly sticky.
Turn the dough out onto a lightly floured surface and knead until smooth but still slightly tacky, 3 to 5 minutes. Oil a large mixing bowl with the remaining 2 teaspoons oil.
Place the dough in the bowl and turn to oil all sides. Cover the bowl with plastic wrap and set in a warm, draft-free place until nearly doubled in size, 1 to 1 1/2 hours.
Divide into 2 equal portions and use as directed.
Yield: 2 (12-inch) deep dish pizza crusts