Melt 1 tablespoon butter in a skillet over medium-low heat. Stir in the onion, celery, and garlic, and cook 5 minutes or until tender.
Melt 4 tablespoons butter in a medium saucepan. Whisk in milk and continue cooking 5 minutes, until sauce is smooth and slightly thickened.
Add cheddar cheese. If sauce is too thick, slowly stir in reserved pasta water until sauce is desired consistency. Season with salt and pepper.
Bake 25 minutes in the preheated oven, or until bubbly and lightly browned.