01 - In a medium saucepan over medium heat, combine the diced peaches, granulated sugar, brown sugar, cinnamon, nutmeg, lemon juice, cornstarch, and salt. Stir continuously until the mixture thickens and becomes glossy, about 5 to 7 minutes. Remove from heat and let cool slightly.
02 - Place an egg roll wrapper on a clean surface in a diamond shape. Spoon about 2 heaping tablespoons of peach filling onto the lower third of the wrapper. Fold the bottom corner over the filling, tuck in the sides, and roll up tightly. Seal the top edge 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 (175°C).
04 - Fry the egg rolls in batches for 2 to 3 minutes per side until golden brown and crispy. Drain on a paper towel-lined plate.
05 - Mix granulated sugar and cinnamon in a shallow dish. Roll the warm egg rolls in the cinnamon sugar mixture until evenly coated.
06 - Serve warm, optionally with a scoop of vanilla ice cream.