2 tablespoons extra-virgin olive oil, plus more for brushing
3 1/2 cups all-purpose flour
1 teaspoon sugar
1/2 teaspoon salt
Kosher salt, for sprinkling
In a small bowl, sprinkle the yeast over 1/2 cup of warm water and let the mixture stand until foamy, 5 to 8 minutes. Stir in the 2 tablespoons of olive oil and 1/2 cup of tepid water.
In a large bowl, combine the flour with the sugar and salt. Make a well in the center and pour in the yeast mixture. Using a wooden spoon, stir slowly to incorporate the dry ingredients into the well. When roughly half of the flour has been incorporated, add 1/3 cup of cool water. When the dough becomes too thick to stir, use your hands to fold it from the side of the bowl toward the center, then flatten it down, repeating the motion until a ball forms.
On a lightly floured work surface, knead the dough until smooth and elastic, about 5 minutes. Transfer the dough to a bowl and cover with plastic wrap. Let rise at warm room temperature until doubled in bulk, about 1 hour. Knead the dough for 3 minutes, then let it rest again until relaxed, about 1 hour.
Preheat the oven to 400°. Lightly oil a large rimmed baking sheet. On a lightly floured work surface, roll the dough into a 14-by-10-inch rectangle. Transfer the dough to the baking sheet, cover with a towel and let rise until doubled in bulk, about 30 minutes.
Using your fingertips, dimple the dough, making indentations all over the surface. Brush with olive oil, sprinkle with kosher salt and bake for 30 to 35 minutes, or until golden brown. Remove from the oven and drizzle with additional olive oil if desired. Transfer the focaccia to a wire rack to cool slightly, then cut into slices or squares and serve.
The focaccia can be made through Step 3 and refrigerated overnight. Bring the dough to room temperature before rolling out.