Spread 1 teaspoon of softened butter on 1 side of an arepa and set it on the griddle, buttered side down. Using a flat spatula, press the arepa into a 6-inch round about 1/3 inch thick; carefully smooth the edges if necessary. Cook the arepa over moderately low heat until browned, about 6 minutes; reduce the heat to low if the arepa browns too quickly. Spread the top of the arepa with 1 teaspoon of butter, flip and cook for 6 minutes longer, or until browned. Transfer the arepa to a plate, sprinkle with cheese and serve. Repeat with the remaining arepas.