Preheat the grill to medium.
In a large bowl, toss the vegetables with olive oil and season with salt and pepper, to taste. Arrange the vegetables on the grill, turning occasionally, until charred and tender, about 10 minutes. Remove to a plate and sprinkle with red pepper flakes.
Slice the bread in half lengthwise with a serrated knife. Toast the bread on the grill Remove the bread and evenly spread Lemon Mayo on both sides. Evenly divide the vegetables on the bottom halves of the bread. Top with the sliced mozzarella and a handful or so of the basil. Cover with the top half of the bread and secure with toothpicks. Slice into 4 portions and serve.
Add the mayonnaise, garlic, lemon zest, lemon juice and salt and pepper, to taste, to a small bowl. Cover with plastic wrap and refrigerate until needed.