Dissolve yeast in water in a large bowl; let stand 5 minutes.
Lightly spoon flour into dry measuring cups; level with a knife. Add 1 cup flour to yeast mixture, stirring well to combine. Cover and let stand at room temperature 8 hours or overnight to create a sponge (mixture will become very bubbly).
Preheat oven to 350°.
Remove papery skin from garlic head (do not peel or separate cloves). Wrap in foil. Bake at 350° for 1 hour; cool 10 minutes.
Separate cloves; squeeze to extract garlic pulp. Discard skins. Place garlic pulp, 1 tablespoon oil, and 1 teaspoon salt in a small bowl, and mash with a fork until smooth. Stir into sponge.
Add 2 cups flour to the sponge; stir until a soft dough forms. Turn dough out onto a floured surface. Knead until smooth and elastic (about 8 minutes); add enough of remaining flour, 1 tablespoon at a time, to prevent dough from sticking to hands (dough will feel tacky).
Place dough in a large bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 45 minutes or until doubled in size. (Gently press 2 fingers into dough. If indentation remains, dough has risen enough.)
Punch dough down. Cover and let rest 5 minutes. Divide dough in half; roll each half into a 10-inch round.
Place 1 dough round on a baking sheet sprinkled with cornmeal. Arrange basil over dough, leaving a 1/4-inch border; top with bell peppers. Sprinkle evenly with cheese. Top with other dough round; pinch edges to seal. Lightly coat with cooking spray. Cover and let rise 45 minutes or until dough is doubled in size.
Preheat oven to 400°.
Uncover dough. Make indentations in top of dough with a knife. Gently brush dough with 1 1/2 teaspoons oil, and sprinkle with 1/4 teaspoon salt. Bake at 400° for 30 minutes or until the focaccia is browned on bottom and sounds hollow when tapped. Remove from pan; cool on a wire rack.