In the bowl of a stand mixer fitted with a dough hook, stir together the warm water and sugar. Sprinkle the yeast on top and stir again. Set aside for 5 minutes, or until the yeast is foamy. If the yeast doesn't foam, discard the mixture and start again with new yeast.

Add the flour and salt and mix on low speed until a shaggy dough forms. Increase the speed to medium and mix for 5 minutes. A very elastic, sticky dough should form and begin grabbing the sides of the bowl.

Brush a large bowl with 2 tablespoons of the olive oil. Transfer the dough to the bowl, using a spatula to scrape it out of the stand mixer bowl. It will be too sticky to transfer by hand. Use your fingers to lightly brush any oil that's pooling at the edges over the dough surface.

Cover the bowl with plastic wrap or a damp towel and set aside until the dough has doubled in size, 1 to 1½ hours.

Brush a 9x13-inch baking dish with another 2 tablespoons of olive oil. Uncover the dough and rub your hands with olive oil. Slide your hand under one edge of the dough and fold it into itself. Continue working around the bowl, folding the dough into itself, until you have a rough ball.

Transfer the dough to the prepared pan and turn to coat in the oil. Press the dough to the pan's edges. Let it relax and pull away from the edges, then press it to the edges again. Cover and set aside to rise until doubled, about 45 minutes.

30 minutes into the second rise, preheat the oven to 425°F.

Remove the plastic wrap and drizzle the remaining 2 tablespoons olive oil over the dough. Rub your hands with olive oil, then use your fingers to make deep indentations across the surface, pressing through the dough to the pan.

Sprinkle with flaky sea salt and rosemary. Bake for 20 to 30 minutes, or until golden brown. Let cool slightly before slicing and serving.