Cook the pasta according to the package instructions. Drain well.
Melt the butter in a saucepan over medium heat. Whisk in the flour and stir for about 1 minute until bubbly and golden brown.
Gradually whisk in the milk until smooth. Bring to a simmer while stirring occasionally. Once the sauce starts to thicken, add in the cheese and whisk until smooth with no lumps. The sauce should be thick and creamy.
Stir in the pasta until it is fully coated with the cheese sauce. Season with salt and pepper to taste before serving.