5 sprigs fresh rosemary leaves, chopped and divided
1 tablespoons granulated sugar
5 1/4 cups all-purpose flour, plus more for kneading
1 tablespoon kosher salt, plus coarse sea salt for sprinkling
1 cup extra-virgin olive oil, divided
In the bowl of a stand mixer, combine the water, yeast, 2 teaspoons of the chopped rosemary, sugar, and half the flour. Stir to combine. Fit the mixer with the dough hook and on low speed add in the remaining flour, salt, and 1/2 cup olive oil. Once the dough comes together, increase the speed to medium and knead for 5 to 6 minutes, or until smooth and soft. If the dough is really sticky, add in another tablespoon or two of flour.
Transfer the dough to a lightly oiled bowl. Cover with plastic wrap and let rise in a warm place until doubled in size, at least 1 hour. Make ahead: place the dough in a large plastic bag, or divide in half and place in two plastic bags, and refrigerate for up to 3 days or freeze for up to 1 month. If frozen, thaw overnight in the fridge or for a few hours at room temperature. Proceed with the recipe.
Coat a jelly roll pan with the remaining 1/2 cup olive oil. Put the dough onto the jelly roll pan (you can divide the dough in half and bake in 2 smaller 9 by 13-inch pans) 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. Spread your fingers to make little holes all the way through the dough.
Cover the dough with plastic and let rise in a warm place until doubled in size, about 1 hour. Meanwhile, preheat the oven to 425?F.
Brush the focaccia with the olive oil on the pan and sprinkle liberally with coarse sea salt and the remaining rosemary leaves. Bake until golden brown, 25 to 30 minutes. Remove from the oven and let cool slightly before cutting and serving.