01 - Combine diced peaches, granulated sugar, brown sugar, lemon juice, cinnamon, nutmeg, and cornstarch in a medium bowl. Mix thoroughly and allow mixture to rest for 5 minutes to macerate, ensuring the fruit releases its natural juices.
02 - Position an egg roll wrapper on a clean work surface with one corner pointing toward you. Place approximately 2 tablespoons of peach filling near the bottom corner. Fold the bottom corner over the filling, fold in both side corners, and roll tightly toward the top corner. Brush the exposed edge with beaten egg and press firmly to seal. Repeat with remaining wrappers and filling.
03 - Pour vegetable oil to a depth of 2 inches in a deep skillet or pot. Heat oil to 350°F. Working in batches to avoid overcrowding, fry egg rolls 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 in a small bowl until completely smooth. Drizzle glaze generously over warm egg rolls immediately before serving.