In a small to medium, heavy-bottomed sauce pan, melt the butter over low heat, stirring occasionally and being careful not to scorch.
Remove from heat. Whisk in corn starch. Gradually add milk, stirring until well mixed.
Return pan to the burner. Cook over low heat, stirring constantly, until thickened and smooth. Cook for another good minute.
Remove from heat (if mixture is boiling, stir and wait until it cools to a smooth surface) and add cheese. Stir until cheese is melted and mixture is smooth and well blended.
Serve with pasta or vegetables.
Just a note about flour: you can use flour in the place of the corn starch, but you'll need to double the about (i.e. for 4 servings, you'll need 2 T. flour in the place of the 1 T. corn starch). Also, you'll need to cook the white sauce for an additional 4 minutes after the sauce thickens (5 minutes rather than 1) before adding the cheese, to cook off the starchy taste.