Melt the butter in a medium pan over medium heat, then add the slowly sprinkle in the flour. Use a wooden spoon to stir well, until it is well combined. Keep stirring this mix for 1 minute on a medium heat. Remove the pan from the heat.
Start by adding 3 tablespoons of the milk. Stirring until it is combined. Then add 1/3 of the milk, again, stir until it is combined. Keep stirring the mixture, it will take a couple of minutes, and you will get lumps. The lumps will go away as you stir. Return the pan to a medium heat, and add the remaining milk. Stir well until the lumps are gone, and the sauce has thickened.
When it has thickened, remove from heat, and slowly add the grated cheese, and stir well.