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 - Pour 2 inches of vegetable oil into a deep skillet or pot and heat to 350°F.
04 - Carefully lower the egg rolls into the hot oil in batches. Fry for 2 to 3 minutes per side until golden brown and crispy. Remove with tongs and drain on a paper towel-lined plate.
05 - Mix the granulated sugar and cinnamon in a shallow dish. Roll each warm egg roll in the cinnamon sugar mixture until evenly coated.
06 - Serve warm, optionally with a scoop of vanilla ice cream on the side.