In a large (5- to 6-quart) bowl, use a wooden spoon to stir together the flour, water, 2 tablespoons of the oil, the sugar, yeast and fine salt until a rough dough forms. Transfer to a container with a lid, partially cover and let rest for about 2 hours on the counter. You can use the dough right away, or cover and refrigerate until needed; see Make ahead. (If you plan on refrigerating and have a lidded container large enough for mixing, you can assemble the dough in there and refrigerate it after the 2-hour rise on the counter. The dough is much easier to handle after being thoroughly chilled.)

Place a baking stone on the middle oven rack and preheat to 425 degrees. Pour 2 tablespoons of oil into a 9-inch cake pan and evenly coat the bottom of the pan.

Dust the surface of the refrigerated dough lightly with flour, then pull half of it off (about 1-pound/454-gram portion; the dusting makes this task easier, as the dough is sticky). Dust the half you are using with more flour and quickly shape it into a ball by stretching the surface of the dough around to the bottom on all four sides, rotating the ball a quarter-turn as you go.

Use your hands to flatten it into a ½-inch-thick round 6 to 7 inches in diameter. Place the dough top side down in the cake pan, moving it around a bit to coat with the oil. It will not fill to the edges of the pan. Turn the dough over, cover the pan with plastic wrap or a plate, and let the dough rest for 10 to 15 minutes.

Use your hands to gently push the dough to the edges of the cake pan. Sprinkle with half of the the rosemary and coarse or flaky salt, as needed.

Re-cover with plastic wrap or plate, and let the dough to rest and rise for 20 minutes.

Repeat with the second ball of dough, or store it to bake later (see Make ahead).

Transfer the cake pan to the heated baking stone in the oven and bake for 20 to 25 minutes, or until the focaccia crust is medium brown and feels dry and firm on the surface. The baking time will vary depending on the focaccia’s thickness. (If baking both loaves at once, switch them from left to right and rotate from front to back halfway through to ensure even baking.)

Use a rounded knife to loosen the loaf from the edges of the pan, then transfer the focaccia to a cutting board. Cut into wedges and serve warm, or allow to cool completely.