Ingredients 1 loaf:
1-3/4 cups water (78 degrees)
3 teaspoons dry active yeast
1/4 cup extra virgin olive oil, divided
3-3/4 cups bread flour
2 teaspoons sea salt
2 cups grated Asiago cheese (6 ounces), divided
10 cloves coarsely chopped garlic
Dissolve the yeast in water in a mixing bowl or workbowl of an electric mixer for 2 minutes. Add 3 tablespoons olive oil and then work in 3-1/2 cups bread flour, 1/2 cup at a time by hand or with the paddle attachment in the machine. Allow the bread to rest for 5 minutes before kneading. Switch from paddle to dough hook. Add remaining flour and salt. Work until the dough is smooth and elastic.
Work in 1-1/2 cups cheese and knead for 1-2 minutes until it is evenly distributed in the dough. Take the dough out of the bowl if working by machine, and slam it down on a clean surface, 3 or 4 times to further tighten the gluten. Place dough in a steep-sided bowl, cover and place in a warm (80 degree) spot to rise for 1 hour, or until doubled.
Punch down and allow the dough to rise for 30 minutes. Lightly dust a 10"x15" bake sheet with cornmeal. Turn out the dough on this prepared surface, and stretch the dough into a 10"x14" rectangle. Spread on the garlic pieces, the remaining tablespoon of olive oil and cheese. Cover the bread with plastic wrap and let rise for 15 minutes.
Preheat a gas grill for 10 minutes to 450 degrees. Uncover the bread, mist the top with water and the inside surfaces of the grill as you open it to put in the bread. Bake for 15 minutes. Check its temperature for an internal reading of 200 degrees. Close the grill and bake 3-4 minutes more as needed. Cool on a rack.