Shred cheddar cheese using a grater and set aside.
In a saucepan, melt butter over medium heat.
Whisk in flour and cook for a minute or two.
Whisk in milk slowly.
Bring to a gentle simmer and whisk until thickened.
Remove from heat or turn heat down to lowest setting, and stir in cheese a little add a time. If your heat is too high, your sauce might "break" and take on a grainy texture.
Season with salt and pepper to taste.
Notes
A block of cheddar cheese will yield better results than pre-shredded cheese. Pre-shredded cheese contains additives that can create a grainy texture when melted into the sauce.TroubleshootingAdd more cheese if you need it thicker or a cheesier flavor.Add a bit more milk if it starts to get too thick.Add more salt if it doesn't "pop" in flavor.