Place baking stone in oven, if using.
Heat oven to 500°F (260℃).
Toss squash, zucchini, and eggplant with olive oil, thyme, salt, and pepper. Set aside.
On a floured surface or parchment paper, roll out dough to form a 12 inch circle.
Top with pesto, leaving a ½ inch border around the edge.
Sprinkle with parmesan cheese.
Top with mozzarella.
Starting on the outer part of the dough and working toward the center, lay alternating vegetables in a circle - zucchini, squash, eggplant, tomato.