In a small saucepan heat olive oil and garlic over medium heat until fragrant and garlic is translucent but not browned; remove from heat and set aside.
Place polenta, sweet peppers, mushrooms, eggplant, zucchini, and summer squash on large baking sheets. Brush polenta and vegetables generously with the garlic oil. Season with salt and pepper. For a charcoal grill, grill polenta slices over medium coals for 4 to 5 minutes on each side or until polenta is lightly browned and heated through, using a metal spatula to carefully turn slices. Grill vegetables directly over medium coals for 4 to 6 minutes or until tender, turning once. (Grill in batches, if necessary.) (For a gas grill, preheat grill. Reduce heat to medium. Place polenta and vegetables on greased grill rack over heat. Cover and grill as above.) Remove from heat and let cool slightly. When cool enough to handle, slice mushrooms.
In a 9-inch springform pan layer grilled vegetables and polenta, starting with eggplant. Sprinkle some of the cheese and a few basil leaves over each layer. Press to compact the layers. Top with tomatoes, more basil leaves, and the remaining cheese. Place torte in a foil pan or wrap the outside of the pan with a double layer of foil. Grill torte over medium-low coals for 15 to 20 minutes or until heated through. (For a gas grill, reduce heat to medium-low. Place torte on grill rack directly over heat. Cover and grill as above.)
Cool on a wire rack for at least 15 minutes. Remove outer ring of springform pan. Use a sharp serrated knife to cut into wedges. If desired, garnish slices with additional basil leaves.