1. Combine the warm water, yeast, and sugar in the bowl of a standing mixer fitted with the dough hook. Let the mixture sit until it begins to look creamy or bubbly, about 5 minutes.
2. Add the olive oil, semolina, all-purpose flour, and salt to the yeast mixture, and mix on medium speed for 10 minutes, until the dough is smooth, scraping the dough hook midway. Transfer the dough to a lightly floured work surface, and knead it two to three times with floured hands to form it into a ball.
3. Oil a large mixing bowl, add the dough, turn to coat with oil, and cover it with plastic wrap. Set the bowl aside in a warm, draft-free place until the dough has doubled in size, about 1 hour.
4. Punch down the dough, and allow it to rise a second time until it has doubled in size, about 1 hour.
5. Divide the dough into two 8-ounce pieces, shape them into balls, and let them rest for about 15 minutes before rolling them out.
Note: If you make this dough way ahead of time, divide it into 8-ounce pieces after the first rise, roll them into balls, cover, and refrigerate until ready to use (up to overnight). The dough can also be frozen for up to 3 months (just thaw it in the refrigerator for several hours before using). Be sure to let the dough sit out at room temperature for 20 minutes or so before rolling it out.
Yield: Two 12- or 14-inch pizzas, or 4 calzones