01 - Combine diced peaches, granulated sugar, brown sugar, lemon juice, cinnamon, nutmeg, and cornstarch in a medium bowl. Stir thoroughly to coat all pieces. Let the mixture stand for 5 minutes to allow flavors to meld and cornstarch to activate.
02 - Position an egg roll wrapper on a clean work surface with one corner pointing toward you. Place 2 tablespoons of peach filling on the lower third of the wrapper. Fold the bottom corner over the filling, fold in the side corners, then roll tightly upward. Seal the final flap with beaten egg. Repeat with remaining wrappers and filling.
03 - Pour vegetable oil to a depth of 2 inches in a deep skillet or heavy-bottomed pot. Heat oil to 350°F. Working in batches to avoid overcrowding, fry egg rolls for 2 to 3 minutes per side until golden brown and crispy throughout. Transfer to paper towels to drain excess oil.
04 - Whisk powdered sugar, milk, and vanilla extract in a small bowl until completely smooth and free of lumps. The glaze should have a thick but pourable consistency. Adjust with additional milk if too thick.
05 - Drizzle warm vanilla glaze over freshly fried egg rolls immediately before serving. For optimal texture and flavor experience, serve while still warm.