Preheat the oven to 350° F. Generously coat 15 wells of two 12-cup muffin pans with nonstick spray. Place the potatoes in a large pot and cover with water. Bring to a boil, reduce heat to medium, and simmer until tender when pierced with a knife, 15 to 20 minutes. Drain, place potatoes in a large bowl, and mash with a potato masher. Fold in the cheese and butter, then add the eggs, salt and pepper.
Divide the potato mixture among the prepared muffins cups, filling them to the top (the cupcakes will not rise in the oven). Bake 40 to 45 minutes or until golden. Cool the muffins in the pans on a rack for 10 minutes before removing from the pans and serving with your favorite baked potato toppings.