In a medium saucepan, melt the butter over medium heat.

Once the butter is melted, add the flour, dry mustard, and cayenne pepper. Whisk the mixture to create a roux; you want to cook the flour for 1 – 2 minutes. The mixture should be thick and clumpy. You need to cook the flour so that you won't taste it later.

Continue to whisk constantly and slowly add the milk. Your sauce should be smooth with no lumps. If you heat your milk, you can add it faster, but if the milk is cold, then add it slowly and constantly whisk.

Reduce the heat to low or take the pot completely off the hot element and add the cheese that you have grated. Stir until the cheese is completely melted into the sauce.

Serve warm however you like. This is the perfect sauce to serve over steamed broccoli or cauliflower.