In a 3-quart / 3 L bowl, whisk 450 g semola rimacinata, the yeast and 8 g salt. Add the warm water and 2 tbsp olive oil and stir until no dry flour remains.

Knead on the counter for 10 minutes until the dough is smooth and slightly tacky, dusting your hands with a little semolina only if it sticks. Return it to the bowl, cover, and let it rise for 60 minutes until doubled.

Warm 2 tbsp olive oil in a 26 cm / 10-inch skillet over medium-low heat. Cook the sliced onion with a pinch of the salt for 10 minutes, stirring now and then, until soft and pale gold, like a quick soffritto.

Add the crushed tomatoes, the remaining salt and the pepper. Simmer for 12 to 15 minutes, stirring, until a spoon dragged across the pan leaves a trail that stays open for a couple of seconds. Tear in the basil and cool the filling completely, about 30 minutes.

Heat the oven to 220 C / 425 F with a rack in the middle and line a 33 x 46 cm / 13 x 18 inch sheet pan with parchment. Dust the counter with semolina.

Divide the risen dough into two pieces of about 385 g each. Roll one piece to a 30 x 40 cm / 12 x 16 inch rectangle about 3 mm thick, keeping the other covered. If it shrinks back, stretch it gently with your hands.

Spread half the cooled filling over the rectangle, leaving a 2 cm border, and scatter with 100 g of the caciocavallo. Starting at a 30 cm short edge, roll tightly into a log, pinch the seam closed and tuck the ends under. Set it seam side down on the pan.

Shape the second piece the same way and place it 5 cm from the first. Prick both logs 6 to 8 times with a fork and brush the tops with 1 tbsp olive oil.

Bake for 28 minutes, rotating the pan after 15 minutes, until the crust is deep golden and the bottoms feel firm when tapped.

Cool on the pan for 10 minutes, then slice into pieces about 4 cm thick with a serrated knife. Serve warm.