In a large bowl, stir together the flour, sugar, baking powder and salt. Pour in the egg, beer and melted butter; stir with a whisk just until blended - a few lumps are okay.
Heat a skillet or griddle over medium heat. Coat with vegetable oil or cooking spray. Spoon about 1/4 cup of batter onto the hot surface for each pancake. When bubbles appear on top of the pancakes, flip, and cook until browned on the other side.