In a bowl, mix vinegar, oil, garlic, shallots, basil, thyme, and rosemary.
Set pizza crusts in 2 pizza pans (12 in. wide) or on 2 baking sheets (12 by 15 in.). Brush crusts equally with all but 2 tablespoons of the vinegar-oil mixture. Layer mushrooms, squash, tomatoes, peppers, and onions equally over crusts. Sprinkle lightly with salt, then equally with mozzarella and parmesan cheeses.
Bake in a 425° regular or convection oven until cheese is lightly browned, 15 to 20 minutes. Drizzle with remaining vinegar-oil mixture. Cut into wedges.