Whisk yeast with warm water in a mixing bowl; whisk in 2 tablespoons olive oil, salt, semolina flour, and 2 teaspoons rosemary until thoroughly combined.

Mix in 2 1/2 cups bread flour until dough is too stiff and sticky to mix.

Turn dough out onto a floured work surface. Knead with the remaining 1/4 cup bread flour as needed until dough is soft, smooth, and slightly elastic, about 3 minutes.

Drizzle dough with 1 tablespoon olive oil and knead briefly for 2 minutes; repeat twice with additional olive oil, kneading for a total of 7-8 minutes.

Drizzle 1 more tablespoon olive oil into a large bowl, place dough inside, and coat with oil. Cover bowl with foil and let rise in a warm place until doubled, 1-2 hours.

Turn dough into an olive-oil-coated sheet pan and press into a rough rectangular shape, pressing out air bubbles; cover loosely with plastic wrap and rest for 15-20 minutes.

Drizzle olive oil onto the dough, poke with oil-covered fingers to create dimples. Let rise again until nearly doubled, 45 minutes.

Preheat oven to 475°F (245°C). Sprinkle rosemary, drizzle olive oil, brush lightly, and sprinkle sea salt.