In a large mixing bowl, combine broccoli, mushrooms, zucchini, and carrots. Drizzle the vegetables with olive oil, and season with salt and pepper. Spread vegetables in a single layer in a shallow baking dish. Roast vegetables in the preheated oven for 30 to 40 minutes; stir halfway through their cooking time. When finished cooking, remove from the oven, and reduce oven temperature to 350 degrees F (175 degrees C).
Bring water, milk, and butter to a boil in a large pot. Remove the pot from heat, and mix in the mashed potato flakes. Let stand two minutes, then stir the mashed potatoes with a fork until they are smooth. Stir in roasted vegetables.
In a dry, nonstick skillet over medium heat, quickly heat each tortilla on both sides to make pliable. Dip the tortillas in enchilada sauce. Put a large spoonful (approximately 1/4 to 1/3 cup) of potato-veggie mixture into the center of each tortilla. Top mixture with about 1 to 2 tablespoons cheese, and roll tortillas. Place seam-side down in a 9x13 inch baking dish. Pour extra sauce over top, and sprinkle with remaining cheese.
Bake at 350 degrees F (175 degrees C) for approximately 20 to 30 minutes, or until the enchiladas are heated through.