Step 1Set a rack in the center of the oven and heat the oven to 450 degrees. Spray 2 baking sheets with nonstick cooking spray.
Step 2Combine the zucchini, squash, mushrooms, shallots, tomatoes, bell pepper, thyme and oregano in a large bowl. Stir in the oil to coat the vegetables and sprinkle with salt and pepper to taste.
Step 3Pour the vegetables into a large roasting pan in a single layer and roast until the vegetables are softened, 15 minutes.
Step 4While the vegetables are roasting, combine the goat, cream and Parmesan cheeses in the bowl of an electric mixer. Add 1 egg and mix on high until smooth, 2 minutes.
Step 5Unwrap the pie crusts and place 1 on each baking sheet. Repair any tears in the dough. Divide the cheese mixture between the crusts, spreading it to within 2 inches of the edges. Spread the vegetables on top of the cheese filling, dividing them between the crusts. Fold in the sides of the crusts to the middle (they won't reach the center) so that each fold overlaps the last slightly to form a rustic-looking tart. Pinch the overlapping edges to seal. Beat the remaining egg and brush it on the crusts to coat.
Step 6Bake the tarts until the crusts are golden brown, 20 minutes.