Combine olive oil, TABASCO® Sauce, salt and garlic in small bowl. Brush vegetables with oil mixture. Grill eggplant, mushroom, zucchini, squash and onion about five minutes, brushing with mixture and turning once. When cool to handle, cut vegetables into bite size pieces.
On floured surface with floured rolling pin, roll pizza dough into two 10-inch round circles, 1/4-inch thick. Carefully place dough rounds on grill. Cover grill; dough will puff slightly in 2-3 minutes. With tongs and spatula, immediately flip dough onto coolest part of grill. Quickly brush the grilled surface of dough with oil mixture. Top dough with grilled vegetables, tomatoes and cheese. Slide pizzas back on hot part of grill. Rotate pizzas frequently so as not to burn. Pizzas are done when top is bubbling and cheese is slightly melted. Serve immediately.
Makes 2 pizzas or 4 servings.