Preheat the oven to 350 degrees F (175 degrees C).
Combine apples, sugar, 1 tablespoon cinnamon, and butter in a bowl.
Wet all edges of wonton wrappers with water. Place 1 tablespoon of apple mixture in center of each wonton. Fold all 4 corners of wonton to the middle. Squeeze together.
Brush egg white onto the wonton wrappers and sprinkle with remaining cinnamon. Place wontons on a baking sheet.
Bake in the preheated oven until golden brown, about 15 minutes.
