Shred the cheddar cheese and set it aside, it should be at room temperature when you add it to the sauce.
Melt the butter over medium heat in a small saucepan.
Whisk in flour. Continue to whisk for 1-2 minutes, until you can no longer smell flour.
Slowly add the milk in splashes, whisking continuously as you do so. Bring to a gentle boil, then reduce to a simmer.
Reduce the heat to low. Gradually sprinkle in the cheddar cheese, whisking constantly as you do so. Continue to whisk until the mixture is well-combined.
Let the sauce continue to heat over low heat, it may appear thin at first but it will continue to thicken upon standing.
Once it's reached your desired level of thickness, remove it from the heat and serve!
Notes
**Colby and Monterey Jack Cheese can also be combined with Sharp Cheddar in this cheese sauce if you want to mix it up!