Preheat oven to 325 degrees. Cut carrots into 1-inch pieces. Bring a pan of water to a boil. Add carrots and cook in boiling water until soft, about 5 minutes. Drain well, then mash. A few larger bits left in the mash is fine.
Melt 1 tbsp. of the butter in a medium skillet over medium-high heat. Add onion and sauté until very soft. Combine carrots, onion, egg, garlic, salt and pepper. Mix well. Spray an 8-inch square baking dish with non-stick cooking spray. Place carrot mixture in prepared dish. Combine crushed crackers with the remaining 1/2 cup butter. Spread crackers over carrot mixture and top with cheese. Bake for 20 to 30 minutes or until mixture is set, and cheese is melted and lightly browned.
Serves 6 to 8