Dissolve yeast and sugar in 1 1/3 cups warm water and 2 tablespoons oil in a large bowl; let stand 5 minutes.
Lightly spoon flour into dry measuring cups; level with a knife. Combine 2 2/3 cups flour, oregano, 1 teaspoon salt, and fennel seeds; stir well. Add flour mixture to yeast mixture, stirring to combine. Turn dough out onto a floured surface. Knead until smooth and elastic (about 5 minutes); add enough of remaining 1/3 cup flour, 1 tablespoon at a time, to prevent dough from sticking to hands (dough will feel sticky). 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 1/2 hours or until doubled in size. (Gently press two fingers into dough. If indentation remains, dough has risen enough.) Press dough out onto a jelly-roll pan coated with cooking spray. Cover and let rise for 30 minutes.
Combine remaining 2 tablespoons oil and balsamic vinegar in a small bowl. Brush oil mixture evenly over zucchini, bell pepper, and onion. Sprinkle with remaining 1/2 teaspoon salt and black pepper. Place vegetables on a grill rack coated with cooking spray. Grill zucchini 4 minutes on each side or until cooked through. Grill bell peppers and onions 6 minutes on each side or until tender. Remove vegetables from grill. Cool completely. Cut bell peppers into 1/4-inch-thick strips.
Preheat oven to 425°.
Arrange vegetables evenly over surface of dough, and sprinkle with cheese. Bake at 425° for 27 minutes or until golden. Sprinkle with basil. Transfer to a wire rack; cool 10 minutes before serving.
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