If grilling the vegetables, bring grill to medium-high heat. Slice thickly (zucchini lengthwise, tomatoes crosswise), brush with olive oil, and season with salt and pepper. Grill until vegetables are softened and browned along their edges.
If roasting the vegetables, set the heat at 325°, lay thickly sliced vegetables in a single layer in a baking dish, and drizzle them with a bit of extra-virgin olive oil; roast for about an hour.
Slice the mozzarella and basil leaves into small pieces and dot with olive oil.
Arrange vegetables on plates, tuck mozzarella and basil leaves in among them, and shake a bit of red pepper flakes over each plate.
This light, flavorful dish can be prepared by cooking the vegetables on an outdoor grill or roasting them in the oven.