Begin by measuring out all your ingredients. Shred the sharp cheddar cheese using your cheese grater and set it aside.
In your medium saucepan, combine the cornstarch with the evaporated milk. Whisk them together until the cornstarch is fully dissolved.
Place the saucepan over medium heat and bring the mixture to a gentle simmer. Stir frequently to prevent the milk from scorching on the bottom.
Once the milk mixture is simmering, gradually add in the freshly shredded cheddar cheese. Stir continuously until the cheese is completely melted and the sauce is creamy.
Add the salt, cayenne pepper, and hot sauce (if using) to the cheese sauce. Taste and adjust the seasonings as necessary.
Once the cheese sauce is smooth and well-seasoned, remove it from the heat. Serve it warm with your favorite tortilla chips, poured over nachos, or as a dip for fresh vegetables.