In small saucepan, combine apples and 1/4 cup water; cook over medium-low heat, stirring occasionally, until apples break down to a sauce-like consistency. Puree in blender, or mash by hand, adding brown sugar, if desired.
Whisk together egg and milk in medium bowl. Add flour; whisk until incorporated. Whisk in butter and granulated sugar to form a batter.
Heat a 10- to 12-inch nonstick skillet over medium heat. Spoon 1 tablespoon of batter per pancake into skillet, leaving 2 inches between each. Cook until edges are golden brown, 1 to 2 minutes. Using a spatula, turn pancakes; cook until golden on bottom, about 1 minute. Serve with a dollop of applesauce on the side, or rolled into a tube.