• In a large bowl, combine the warm water, yeast, and sugar. Add in 2 teaspoons of the chopped rosemary, half the flour, and the salt, and stir to combine. Add 1/2 cup olive oil. Gradually add in the remaining flour until a shaggy mass forms. Only add in as much flour as you need to create a shaggy, slightly sticky dough.
• Transfer the dough to a lightly oiled bowl. Cover with plastic wrap and let ferment at room temperature for about 8 to 10 hours, or until doubled in size. At this point, you can refrigerate the dough for several days until ready to bake. This will also develop more flavor.
• Coat a rimmed half-sheet pan with the remaining 1/2 cup olive oil. Turn the dough onto the pan and begin pressing it out with your fingertips to fit the size of the pan. Coax and stretch the dough to fit the entire pan, or just about. If the dough springs back, cover and let it rest for 10 minutes before proceeding. Spread your fingers to make little dimples all the way through the dough. 

Make the brine:

• Combine the warm water and salt together until the salt is dissolved. Pour all over the dough to make little pools of water in the dimples. Cover loosely with plastic and allow to rise again until the dough is puffy, about 45 minutes.

Bake the bread:

• Meanwhile, place a baking stone in the oven and preheat to 450°F. If you don't have a baking stone, invert a heavy-duty rimmed baking sheet and place in the oven to preheat.
• Sprinkle the dough liberally with coarse sea salt and the remaining rosemary leaves. Bake with the sheet pan on top of stone until the focaccia is golden brown, 25 to 30 minutes.