01 - Combine diced peaches, granulated sugar, brown sugar, lemon juice, cinnamon, nutmeg, and cornstarch in a medium bowl. Mix thoroughly and allow the mixture to sit for 5 minutes to macerate, ensuring the flavors meld together.
02 - Position an egg roll wrapper on a clean work surface with one corner pointing toward you. Place approximately 2 tablespoons of peach filling just above the bottom corner. Fold the bottom corner over the filling, fold in the sides, and roll tightly upward. Seal the final corner with a brush of beaten egg. Repeat this process with all remaining wrappers and filling.
03 - Pour vegetable oil into a deep skillet or pot to a depth of 2 inches. Heat the oil to 350°F. Fry the egg rolls in small batches for 2-3 minutes per side until they achieve a golden-brown, crispy exterior. Transfer to paper towels to drain excess oil.
04 - Whisk together powdered sugar, milk, and vanilla extract in a small bowl until smooth and free of lumps. Drizzle the glaze generously over the warm egg rolls just before serving.