Lightly oil a baking sheet with 2 teaspoons of the olive oil.
In the bowl of a standing electric mixer fitted with a dough hook, combine the water, sugar, and yeast with 4 tablespoons of the remaining olive oil. Stir and let sit until foamy, about 5 minutes.
Add the flour and regular salt and mix on low speed until the dough comes together and forms a ball, about 2 to 3 minutes.
Increase speed to medium and mix for 7 to 8 minutes. If the dough is a little sticky, continue mixing and, with the mixer on low speed, add a bit more bread flour to form a smooth, elastic dough.
Coat a large mixing bowl with 1 teaspoon of the remaining olive oil. Transfer dough to the bowl and turn to coat evenly with the oil. Cover the bowl with a damp clean kitchen towel or plastic wrap and put in a warm, draft-free area to rise until dough has doubled in size, about 1 1/2 hours.
Position rack in center of oven and preheat the oven to 450º F.
When the bread dough has doubled, punch the dough down with your fist and transfer to the greased baking sheet. Using your fingers, press the dough evenly to about 1/2-inch thickness.
Cover with plastic wrap, put in a warm, dry area, and let rise until doubled in size, about 30 minutes to 1 hour.
Remove the plastic wrap and, using your fingertips, press to form dimples in the dough at about 3-inch intervals. Sprinkle with the kosher salt and drizzle with the remaining 2 tablespoons of olive oil.
Bake until golden, about 25 to 30 minutes. (You may need to turn the baking sheet once during the cooking time to ensure even browning.)
Using oven mitts or pot holders, remove the baking sheet from the oven and transfer to a wire rack. Sprinkle the focaccia with the chopped basil and set aside to cool.
YIELD: 1 large "loaf" of focaccia, about 12 inches by 17 inches