In a medium saucepan, melt the butter over medium-low heat. Add the flour and whisk until it forms a paste. Cook for 2 minutes while stirring continuously.

First, add a 1/4 cup of milk and whisk until smooth. Repeat until you have added 1 cup of milk. Add the remaining milk and mix well. Increase heat to medium-high and bring to a boil while stirring constantly.

Let it boil for 1 minute and remove from the heat.

Add the cheese, salt, Dijon mustard, and cayenne pepper. Stir until the cheese melts.