Pour 1/3 cup warm water into a bowl; sprinkle yeast over 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 yeast mixture; mix with your hands to form a relatively stiff dough ball, adding more water if needed to bring dough together.

Transfer dough to a work surface; knead until smooth, about 5 minutes. Cover with the bowl; let rest for 30 minutes.

Uncover dough; knead 3 to 4 minutes. Divide dough into 2 portions; shape each into smooth balls, using damp hands to help smooth out dough, if needed.

Generously dust half a kitchen towel with semolina flour; place dough balls on top. Sprinkle dough ball tops with semolina flour; cover with other half of towel. Let dough rise until almost doubled in volume, about 2 hours.

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

Roll out each dough ball on a lightly floured surface into a very thin circle or oval shape.

Combine pizza sauce and basil in a bowl; spread a thin layer of sauce over dough, leaving a 1 inch border. Scatter provolone every few inches over sauce. Fold opposite dough edges toward the middle to form a rectangle; press lightly to flatten slightly. Repeat spreading sauce and scattering provolone over dough.

Fold each end toward the center to make a square shape. Spread with a thin layer of sauce and scatter pieces of cheese on one half. Fold in half, overlapping the edge by about 1 inch. Transfer to the prepared baking sheet. Repeat filling and folding (Steps 8 and 9) with remaining dough, sauce, and cheese.

Bake in the preheated oven until very well browned, 16 to 18 minutes. Some spots may get charred, but this is fine and desirable, since scacce are traditionally cooked in very hot wood-fired ovens. Let rest before slicing and serving, 15 minutes.