In a small saucepan, combine cheddar cheese and cornstarch. Toss until cheese is evenly coated.
Stir in evaporated milk and salt and pepper to taste (I like 1 teaspoon salt, and 1/4 teaspoon pepper). Heat over medium-high heat, whisking occasionally, until cheese is melted and smooth, about 3 to 5 minutes.
Reduce heat to low, cover, and keep warm until serving time. Or, transfer to a slow cooker on the "warm" setting for serving.
Shredded cheese: It's okay to use pre-shredded cheese here. Although they are tossed with agents to prevent the cheese from sticking together, it will still melt and thicken up fine.
Yield: This recipe makes about 2 cups.
Storage: Store leftovers covered in the refrigerator for up to 4 days.
Slow cooker: Make the recipe as directed below, on the stove, and then transfer it to your favorite slow cooker (I used one of the "mini sizes" and there is room for a double batch of this cheese sauce recipe). I've left it on the "warm" setting for a few hours and all it ever needs is a little stir. It works really well!
Spicy: You can stir in a can 4-ounce of diced green chiles, drained, for some extra flavor and heat. You can do that on the stove or in a slow cooker. If you add them to the slow cooker, just be sure the cheese sauce is back to "hot" before serving (the chiles might cool it down temporarily).