On a baking sheet, toss together the eggplant, zucchini, shallots, garlic, olive oil, vinegar, salt, and pepper. Roast until veggies begin to brown and are tender when pierced with a fork, about 20 - 25 minutes. Transfer veggies to a bowl and set aside.
Change oven temperature according to directions for pizza dough. Roll out the dough into one large rectangle and place on the same baking sheet used for the veggies. Fold over a crust around the edges and pinch down with a fork. Pre-bake dough if pizza crust recipe calls for it.
Smear the pizza sauce in one even layer on top of the dough. Sprinkle with the mozzarella and then about half the veggies (save the rest of the veggies for another day. I figured it's better to be left with cooked veggies than half a raw eggplant and zucchini!).
Add the ricotta in dollops on top and bake according to pizza crust directions. At the end, broil on high for 1 minute to brown the ricotta.
Sprinkle with fresh basil leaves and Parmesan cheese and serve.