Melt butter in a skillet over medium heat. Add apples, brown sugar, cinnamon, and nutmeg. Cook until apples are tender, about 5-7 minutes. Remove from heat and let cool slightly.

Place one egg roll wrapper on a clean surface with a corner pointing towards you. Spoon 2 tablespoons of apple mixture in the center.

Fold the bottom corner over the filling, fold in the sides, and roll tightly. Brush the top corner with beaten egg to seal. Repeat with remaining wrappers and filling.

Heat oil in a skillet over medium heat. Fry egg rolls until golden brown, 2-3 minutes per side. For a lighter version, bake at 400°F (200°C) for 15-20 minutes, turning halfway.

Let cool slightly. Dust with powdered sugar or drizzle with caramel sauce. Serve warm with ice cream or whipped cream if desired.