Stir together ½ cup warm water and sourdough starter in a medium bowl until starter is mostly dis- solved. Add white whole-wheat flour and semola flour. Stir until mixture is smooth. Cover bowl with a clean towel, and let stand at room temperature until levain is bubbly, smells fruity, and is at least doubled in volume, about 4 hours. Make the dough:

Stir together levain and 2¼ cups room-temperature waterin a large bowl until levain is mostly dissolved. Add white whole-wheat flour and semola flour. Mix with your hands until all ingredients are incorporated and there are no dry spots. Cover bowl with a clean towel, and let stand at room temperature 30 minutes.

Sprinkle dough with salt, and add remaining ½ cup room-temperature water to dough in bowl. Using a squeezing motion, incorporate salt and water into dough. Stretch and fold dough over itself in bowl until it begins to feel tight and is no longer elastic, 4 to 6 minutes. Add oil, and continue stretching and folding until oil is incorporated and dough forms a tight ball, about 1 minute. Cover bowl with a clean towel, and let stand at warm room temperature (about 80°F) until doubled in volume, 3 to 4 hours, performing 1 set of stretch and folds (4 folds per set, rotating bowl 90 degrees after each fold) every 30 minutes.

Turn dough out onto a lightly floured (with white whole-wheat flour) work surface. Divide dough evenly into 4 pieces (about 1 pound each). Shape each piece into a ball. Cover with a clean towel, and let rest 10 minutes.

Lightly grease (with oil) 2 (11-inch) disposable aluminum baking pans or 2 (12-inch) aluminum pizza pans. Working with 1 dough ball at a time and keeping remaining dough balls covered, roll dough into an 11-inch round. Transfer dough round to 1 prepared pan, and stretch with your fingers to cover the base of the pan. Repeat process with a second dough ball and remaining prepared pan. Cover each pan with a clean towel. Let stand at warm room temperature (about 80°F) until dough has relaxed and slightly increased in volume, 30 to 45 minutes.

Arrange half of cheese slices (12 ounces) evenly over the 2 dough rounds in pans, leaving a ¾-inch border in each. Top evenly with broccoli, sausage, shallot, olives, and sun-dried tomatoes. Sprinkle evenly with salt, and top evenly with remaining 12 ounces cheese.

Preheat oven to 400°F. Roll out remaining 2 dough balls into 11-inch rounds. Place dough rounds on top of assembled pies so that edges of top rounds just cover the edges of the fillings. Working with 1 pie at a time, twist the edge of the bottom dough round up and over the edge of the top dough round, pressing to adhere. Continue around the edge of pie to fully seal and create a twisted rope pattern. Cover pies with clean towels, and let stand at warm room temperature (80°F) until slightly increased in volume, about 30 minutes.

Brush pies lightly with oil. Using a knife, cut a 1-inch hole in top of each pie to allow steam to escape. Bake in preheated oven until golden brown, 35 to 40 minutes. Remove from oven. Brush tops of pies lightly with oil. Let cool 10 minutes. Slice and serve.