Heat the grill to a medium heat - about 425°-450°.
Depress a 4" wooden skewer into the side of the sliced vidalia onion so that it pierces all the interior rings and holds them together like a lollipop (that's so the onion doesn't fall apart and slip through the grill grates.)
Use a sharp knife to trim the top and bottom of the bell peppers so that its hollow when you look through it. Make a slit along one side of the pepper and lay it flat on a cutting board. Trim the ribs and seeds from the pepper and discard.
Brush the zucchini, squash, peppers and onion with the olive oil and sprinkle lightly with salt and pepper.
Place the vegetables on the grill and cook for 2-3 minutes on the first side before flipping them and grilling for an additional 2 minutes on the other side. Transfer the grilled vegetables to a sheet pan to rest.
Slice the mozzarella into 1/4" slices and if you'd like a more uniform look - use a small 2" biscuit cutter to cut the mozzarella into rounds. (the leftover bits are for the chef to enjoy).
Use a medium platter with a rim to layer the vegetables, tomatoes and mozzarella. Drizzle the the aged balsamic.
Stack the basil leaves on top of one another and roll into a tight "cigar" shape. Thinly slice the basil, crosswise to create a chiffonade and sprinkle over the platter of vegetables. Serve at room temperature or slightly chilled.
Serve at room temperature or slightly chilled. Can be made several hours before serving, covered and refrigerated.