Preheat the grill to high heat and brush the grill with a little bit of oil.
In a medium bowl, combine zucchini, red pepper, mushrooms, and red onion. Drizzle with olive oil and toss to coat. Season with salt and pepper. Place vegetables evenly on a grill pan that has been coated with cooking spray. Grill for 8 minutes or just until tender. Remove from grill and set aside.
Roll the pizza dough into a large oval on a lightly floured surface. Place the pizza dough on a lightly floured rimless baking sheet, or pizza peel.
In a small bowl, combined the melted butter and minced garlic. Brush the pizza dough with the garlic butter.
Slide the pizza dough directly onto the hot grill. Grill the pizza dough for about 2 minutes with the lid closed. Open the grill lid and flip the pizza carefully with a pair of tongs. Grill for 2-3 minutes more. The dough should be golden brown with grill marks on both sides. Remove the pizza from the grill.
Sprinkle fresh mozzarella cheese over the pizza, leaving a 1/2-inch border around edges. Arrange grilled vegetables evenly over the cheese. Grill pizza 3-5 minutes or until cheese melts and crust is golden brown. Remove pizza from grill and top with fresh tomatoes and basil.
Cut into slices and serve.
Note-if you don't have a grill, you can make this pizza in the oven. You can roast the vegetables at 400 degrees F and cook the pizza at 500 degrees F.