In a medium saucepan over medium heat, melt the butter and add diced peaches, brown sugar, cinnamon, and nutmeg.
In a small bowl, whisk cornstarch and water to create a slurry; stir into the peach mixture.
Cook the peach filling for 3 to 5 minutes until the liquid thickens and peaches are tender, then remove from heat and let cool completely.
Lay an egg roll wrapper on a clean surface in a diamond shape and place 2 tablespoons of peach filling in the center.
Fold the bottom corner over the filling, tuck in the side corners, and roll tightly towards the top corner.
Brush the top corner with egg wash to seal the roll completely.
Heat vegetable oil in a deep fryer or heavy pot to 350 degrees Fahrenheit.
Fry the egg rolls in batches for 2 to 3 minutes per side until golden brown and crispy.
Drain on paper towels and dust with powdered sugar before serving.