1. Whisk water, 2 tablespoons oil, and yeast together in liquid measuring cup until yeast dissolves. Whisk flour and 2 teaspoons salt together in bowl of stand mixer.
2. Using dough hook with mixer on low speed, slowly add water mixture and mix until dough comes together, about 2 minutes. Increase speed to medium and continue to mix until dough is smooth and elastic, about 8 minutes. (If after 4 minutes dough is still very sticky, add 1 to 2 tablespoons extra flour; dough should clear sides of bowl but stick to bottom.)
3. Transfer dough to lightly greased bowl, cover tightly with greased plastic wrap, and let rise for 30 minutes.
4. Gently press center of dough to deflate. Using greased bowl scraper (or rubber spatula), fold partially risen dough over itself by gently lifting and folding edge of dough toward middle. Turn bowl 90 degrees and fold dough again; repeat turning bowl and folding dough 1 more time. Cover with plastic and let rise for 30 minutes.
5. Grease 12-inch cast-iron skillet with 2 tablespoons oil. Transfer dough to prepared skillet, top side down, sliding dough around skillet to coat with oil. Cover with plastic and let rise for 30 minutes.
6. Adjust oven rack to middle position and heat oven to 500 degrees. Using fingertips, press dough out toward edges of skillet. Using fork, poke entire surface of dough 25 to 30 times. Drizzle with remaining 1 tablespoon oil and sprinkle with rosemary and remaining 1 teaspoon salt. Let dough rest for 10 minutes.
7. Transfer skillet to oven and reduce oven temperature to 450 degrees. Bake until top of loaf is golden brown, 23 to 26 minutes, rotating skillet halfway through baking.
8. Using potholders, transfer skillet to wire rack and let loaf cool for 10 minutes.
9. Being careful of hot skillet handle, remove loaf from skillet, return to rack, and let cool for at least 20 minutes before serving.