Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add cauliflower and carrots, cover, and steam until tender, 4 to 6 minutes. Drain and set aside.
Preheat oven to 350 degrees F (175 degrees C).
Melt 2 tablespoons butter in a large skillet over medium heat. Stir flour into butter to make a smooth mixture; cook for 1 minute. Stir milk, sugar, salt, and black pepper into the flour mixture; continue cooking and stirring until the sauce thickens, 2 to 3 minutes. Fold cauliflower, carrots, peas, onion, green beans, green bell pepper, and garlic into the sauce to coat. Mix 1 cup Cheddar cheese into the vegetable mixture. Transfer the mixture to a 2 1/2-quart casserole dish. Sprinkle remaining Cheddar cheese over the dish.
Bake in preheated oven until top is golden and cheese is bubbly, about 30 minute.