Preheat oven to 350 F. Cook pasta according to package directions, drain.
In a large saucepan over medium heat, melt butter. Add in flour and cook for a minute to brown. Add milk, 2 cups shredded cheddar cheese, salt and pepper.
Whisk constantly until smooth and thickened. Mix sauce with the cooked pasta and spread out into a large greased baking dish. Top with the remaining 2 cups shredded cheddar cheese. Bake for 30 minutes.