In a medium non-stick skillet melt enough butter to just coat the bottom of the pan over medium heat. Sprinkle a fine layer of grated cheese in a circular pattern over the bottom of the pan and shake the pan to evenly distribute, as though making an omelet. Cook over medium heat until it has melted and formed a light crust, 3 to 4 minutes. Continue to cook until the edges set and a golden crust develops, 30 seconds to 1 minute. Gently lift and turn with a spatula or fork and cook until lightly golden on the second side, 2 to 3 minutes, being careful not to let it burn.
Remove the frico from the pan and either set it flat on a paper towel, shape it over an inverted custard cup, or drape over a rolling pin or dowel. Continue with the remaining cheese.