To prepare dough, dissolve yeast in warm water in a large bowl. Stir in 2 tablespoons oil, and let stand 5 minutes. Lightly spoon all-purpose flour into dry measuring cups; level with a knife. Add 3 1/2 cups flour and salt to yeast mixture; stir until a dough forms. Turn dough out onto a lightly floured surface. Knead until smooth and elastic (about 10 minutes); add enough of remaining flour, 1 tablespoon at a time, to prevent dough from sticking to hands.
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, 1 hour or until doubled in size. (Gently press two fingers into dough. If indentation remains, dough has risen enough.) Punch dough down; cover and let rest 5 minutes.
While dough rises, prepare topping. Place zucchini, bell peppers, and onion in a large bowl; stir in 1 tablespoon oil and black pepper, tossing well. Place on grill rack coated with cooking spray; grill 5 minutes on each side or until tender. Remove from grill; stir in garlic.
Divide dough into 6 equal portions, pressing each portion into a 7-inch round. Coat both sides of dough rounds with cooking spray. Place 3 dough rounds on grill rack. Grill 4 minutes or until puffed and golden. Remove from grill. Turn rounds over; top each round with 1 tablespoon mozzarella, about one-sixth of vegetables, and 1 tablespoon Gruyère cheese. Place topped rounds on grill. Cover and cook 1 1/2 minutes or until bottoms are browned. Repeat procedure with remaining 3 dough rounds, vegetables, and cheeses.