Adjust the oven rack to the lower third position and preheat the oven to 350°F degrees. Lowering the oven rack prevents the top of your bread from browning too much too soon. Spray a 9×5 inch loaf pan with non-stick spray. Set aside.
Preheat oven to 400 degrees. Mix all ingredients (use 1.5 cups cheese), and place in 9×14 baking dish. Top with 0.5 cup cheese and cover with foil. Bake 25 minutes. Remove foil and bake an additional 20-25 minutes or until top is bubbly and browned.
Preheat oven to 425°F (230°C). Toss squash and carrot with olive oil and arrange on 2 rimmed baking sheets, being sure not to overcrowd the sheets. Roast until squash and carrot are very well browned on a couple of sides, about 40 minutes; use a thin metal spatula to turn pieces 2 or 3 times during cooking. Set aside.