1. Combine 1-1/4 cups of the all-purpose flour, the yeast, sugar, and salt in a large mixing bowl. Add water and olive oil. Beat with an electric mixer on low speed for 30 seconds, scraping sides of bowl. Beat on high speed for 3 minutes. Stir in the 1-1/4 cups semolina and as much of the remaining all-purpose flour as you can with a wooden spoon.
2. Knead in enough remaining all-purpose flour to make a moderately stiff dough that is smooth and elastic (6 to 8 minutes total). Shape dough into a ball. Place in a greased bowl, and turn once to grease entire surface of dough. Cover and let rise in a warm place until double in size (about 1 hour).
3. Punch down dough; divide in half. Cover and let rest 10 minutes. Grease two baking sheets. Shape each half of dough into a ball. Place on the prepared baking sheets. Flatten each ball to about 6-1/2 inches in diameter. Cover and let rise until nearly double in size (30 to 45 minutes).
4. Preheat oven to 375 degrees F. Rub loaves lightly with additional semolina. Cut a crisscross in the top of each loaf. Bake about 25 minutes or until golden and the bread sounds hollow when lightly tapped. Transfer loaves to wire racks; let cool. Makes 2 loaves (8 servings per loaf).
Make-Ahead Tip: Place cooled loaves in a container or bag. Store at room temperature for up to 2 days or freeze for up to 3 months. Thaw frozen loaves in container or bag at room temperature for 1 hour, then wrap them in foil and warm them in a 350 degree F oven for 10 to 15 minutes.