01 - Combine peaches, granulated sugar, brown sugar, lemon juice, cinnamon, nutmeg, and cornstarch in a medium bowl. Mix thoroughly and let stand for 5 minutes to allow flavors to meld and juices to release.
02 - Place an egg roll wrapper on a clean work surface with one corner pointing toward you. Spoon 2 tablespoons of peach filling near the bottom corner. Fold the bottom corner over the filling, fold in the sides, and roll tightly upward. Seal the final corner with beaten egg. Repeat with remaining wrappers and filling.
03 - Heat 2 inches of vegetable oil in a deep skillet or pot to 350°F. Fry egg rolls in batches for 2-3 minutes per side until golden brown and crispy. Transfer to paper towels to drain excess oil.
04 - Whisk together powdered sugar, milk, and vanilla extract until smooth and lump-free. Drizzle glaze over warm egg rolls immediately before serving.