Cut the eggplant into 1/2 inch slices. Cut the zucchini in half crosswise. Cut each half into 1/4 inch slices.
Lay the eggplant and zucchini slices on a baking sheet. Brush on both sides with olive oil and season with salt and pepper.
Transfer to grill and grill until the vegetables are tender, but not overcooked, about 4 minutes per side for the eggplant and 3 minutes per side for the zucchini.
In the last 30 seconds of cooking, divide the mozzarella evenly and top the eggplant rounds. Re-close the barbecue lid and cook for additional 30 seconds, or until the mozzarella is melted onto the eggplant.
Lay one eggplant round on a large platter. Top with 1 tsp tomato sauce. Next, add a pinch of basil, then add a slice of zucchini.
Continue stacking in this order, ending with an eggplant round and tomato sauce. Spoon any remaining tomato sauce on top of the assembly.