In a saute pan, melt the butter over a medium-low heat. Sift in the flour and mix until well
Add the milk and turn the heat to medium-high. Whisk the mixture until well combined.
Add the salt and cayenne pepper.
Once the mixture begins to simmer, reduce to medium heat. Adjust as needed to keep a low simmer. Cook for 2 minutes. The sauce should thicken.
Remove the pan from the heat. Add in a handful of the cheese and mix until it is fully melted and incorporated. Repeat until all of the cheese has been incorporated.
If you keep heat during this step, you risk the cheese breaking.