Pour 1/3 cup warm water into a mixing bowl; sprinkle yeast over the top. Let stand to make sure yeast is active, 10 to 15 minutes.

Add 1 1/2 cups semolina flour, olive oil, and salt to the yeast mixture; mix with hands to form a relatively stiff dough ball, adding more water if needed.

Knead the dough on a work surface until smooth, about 5 minutes. Cover with a mixing bowl and let rest for 30 minutes.

Knead the dough again for 3 to 4 minutes and divide into 2 portions. Shape each into a smooth ball and let rise until almost doubled in size, about 2 hours.

Preheat oven to 500°F (260°C). Line a baking sheet with foil and sprinkle with cornmeal.

Roll each dough ball into a thin circle or oval shape. Combine pizza sauce and basil, spreading thinly over the dough, and scatter provolone cheese pieces randomly.

Fold opposite dough edges to form a rectangle, press lightly, and repeat the filling and folding process until you've created a square shape. Spread additional sauce and cheese on one half and fold in half to form layered dough.

Transfer to prepared baking sheet. Repeat with remaining dough. Bake in the preheated oven until well browned, 16 to 18 minutes.