In a small saucepan, melt the butter over low-medium heat. Once fully melted, sprinkle the flour on top of the melted butter and mix with a spatula until fully incorporated and a paste has formed. Continue mixing for 1-2 minutes.
Slowly pour in the milk while continuously whisking. When the mixture has thickened enough to coat the back of a spoon, add in the cheese and whisk until the cheese has all melted and mixture is uniform.