In a small saucepan over medium high heat, melt the butter, stirring frequently.
Whisk cornstarch into butter, until smooth, lowering heat as needed.
Slowly whisk milk into butter mixture and continue to stir for 3-4 additional minutes, until turns into a thickened sauce.
Add cheese to milk mixture, and stir just until melted smooth. Add pepper, and stir.
Use as a dipping sauce for pretzels, or as a cheese sauce for nachos.
You can use pre-grated store-bought cheese, but it does have an anti-caking agent and causes the dip to have a little bit of a grainy starchy texture. Use freshly grated cheese for best quality and results.
Best served fresh, but may be stored in refrigerator up to 3 days and reheated in a saucepan over medium-low heat.