To make the dough, brush a 13-by-18-inch rimmed baking sheet with 3 tablespoons oil and sprinkle with 2 tablespoons semolina; set aside. In a 1-quart liquid measuring cup, combine 2 cups water and 2 tablespoons of the remaining oil.

In a stand mixer with the dough hook, mix the remaining 128 grams (¾ cup) semolina, the bread flour, sugar, salt and yeast on low until combined, about 30 seconds. With the mixer running, gradually add the water-oil mixture, then mix until well combined, about 2 minutes. Increase to medium and knead, scraping the bowl once or twice, until the dough pulls away cleanly from the sides, about 5 minutes. Using a bowl scraper or silicone spatula, scrape the dough onto the center of the prepared baking sheet. Brush the remaining 1 tablespoon oil evenly over the dough’s surface. Press a sheet of plastic wrap against the surface of the dough and let rest at room temperature for 30 minutes.

Uncover the dough. With dampened fingertips, gently push and stretch the dough to the edges and into the corners of the baking sheet; try not to press out any bubbles. The dough will not completely fill the baking sheet, but should come close. Re-cover with the plastic wrap and let rest for another 30 minutes.

Again using dampened fingertips and working outward from the center, spread the dough into an even layer to the edges and into the corners of the baking sheet. Re-cover and let rest until the dough is bubbly and risen by about half, 20 to 25 minutes. Meanwhile, heat the oven to 500°F with a rack in the lower-middle position.

While the dough rests and the oven heats, make the tomato sauce. In a small saucepan over medium, combine the oil, garlic and pepper flakes; cook, stirring, until the garlic is golden and fragrant, about 2 minutes. Add the tomatoes, ½ cup water and ½ teaspoon each salt and black pepper. Bring to a simmer over medium-high, then reduce to medium and simmer until thickened and reduced to about 1½ cups, about 15 minutes. Set aside until ready to use.

When the dough is ready, uncover it and spread the tomato sauce evenly over the surface, nearly to the edges. Sprinkle with the fontina and pecorino, then scatter on the pepperoni (if using) and pickled peppers (if using).

Bake until golden brown and the edges are deeply caramelized, about 25 minutes. Cool in the pan on a wire rack for 10 minutes. Using a wide metal spatula, loosen the sides and bottom, then slide onto a cutting board. Slice into 12 pieces.