Add zucchini, squash, cheese, mushrooms, tomato, onion, oil, oregano, basil, pepper, and salt to a large bowl and combine well.
Cut 8 (15-inch) square pieces out of parchment paper. Fold each piece in half and then open flat. Spoon about 1 cup of vegetables in the center of each piece of parchment. Fold parchment in half seal the edges. Move pouches to a baking sheet.
Bake for 20 minutes or until pouches are puffed up and golden. Cut open pouches to let out some steam before serving.