Preheat oven to 350°F. Place prepared head of garlic on a piece of foil big enough to wrap it entirely. Wrap in foil and place on a baking sheet and roast for 50 minutes. Remove from the oven and place in refrigerator.
To prepare the dough, place 1 cup of the warm water, sugar and yeast in a large bowl. Stir together, and let the mixture sit for 5 minutes with a towel on top.
Stir in the remaining water, ¼ cup olive oil and salt. Stir in flour, 1 cup at a time, until a dough forms. With floured hands, remove dough from mixing bowl and place on a floured surface. Knead dough for 4 minutes, adding a little more flour (1 tablespoon at a time) if it’s too sticky to work. After kneading, dough should spring back when poked.
Place dough in another large bowl that has been greased with olive oil. Coat the top with a little oil, as well. Cover bowl with a towel or plastic wrap and place in a warm place to rise for 2 hours, or until it’s doubled in size. Once risen, grease an 12- by 17-inch edged baking pan with 3 tablespoons of olive oil. Use your hands to gently flatten and spread the dough into the pan. Use your fingers to poke deep holes in the top of the dough.
Peel roasted garlic and place in a small bowl. Add remaining 3 tablespoons of olive oil and use a fork to smash the garlic and combine it with the oil. Brush this mixture on the top of the dough. Place your focaccia in the oven to bake for 20–23 minutes or until the top is golden brown and crispy. Remove from the oven, slice and enjoy.