In a bowl or jar, whisk the lukewarm water and sugar, then sprinkle the yeast on top. Stir once, cover, and let sit for about 10 minutes, or until foamy and doubled in volume.
Add the activated yeast mixture to a stand mixer fitted with a dough hook. Add the flour, salt, and 1 tablespoon olive oil. Mix on low until the dough pulls away from the sides and feels slightly sticky, about 2–4 minutes. Shape into a ball, place in a lightly greased bowl, cover, and let rise in a warm spot for 1 hour or until doubled.
Punch down the dough, fold the edges toward the center, and shape into a smooth ball again.
Grease a baking pan with 2 tablespoons olive oil (it should look generously coated). Set aside.
Roll the dough on a silicone mat or lightly floured surface to about ½-inch thickness, then transfer immediately to the oiled pan. Cover and let rise again for 45–60 minutes, or until puffy and doubled.
Preheat the oven to 350°F. Use your fingertips to dimple the dough all over. Brush with the remaining 2 tablespoons olive oil, press in rosemary, and sprinkle with flaky salt.
Bake for about 22 minutes, or until golden and cooked through.