Combine the warm water, sugar, and yeast in a bowl and stir until the yeast and sugar are dissolved. Let them sit for about 5 minutes, or until the mixture develops a layer of foam on top.
While the yeast is proofing, combine 1 cup of the flour and the salt in a large bowl. Stir to combine.
Pour the yeast mixture and olive oil into the bowl with the flour and salt. Stir until the slurry is smooth and free of lumps. Begin adding more flour, about 1/3 cup at a time, until the mixture turns into a ball of dough (about 2 cups total flour).
Turn the dough out onto a clean surface that is lightly dusted with flour. Knead the dough until it is smooth and no longer sticky, adding only small amounts of flour as you go (about 5 minutes total). Return the ball of dough to the mixing bowl, cover with plastic, and let sit for one hour or until double in size.
Preheat the oven to 375ºF. Prepare a baking sheet by sprinkling a liberal amount of cornmeal over the surface (about 2 tbsp). Punch down the risen dough, then stretch it over the baking sheet, leaving the dough about 1/4-1/2 inch thick.
Place the butter and minced garlic in a small dish and microwave for 30 seconds or until the butter is melted. Brush the butter and garlic mixture over the surface of the dough. Sprinkle the grated Parmesan over the butter and garlic. Finally, add the shredded cheese in an even layer over everything.
Bake the bread for about 15 minutes in the preheated oven, or until the cheese is melted and is just beginning to turn golden brown on the edges. Once baked, slice the cheesy garlic bread down the center lengthwise, then across into ten strips, about 1-inch wide.