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 the peach filling onto the lower third of the wrapper. Fold the bottom corner over the filling, tuck in both sides firmly, and roll up tightly. Seal the top edge with beaten egg. Repeat with the remaining wrappers and filling.
03 - Pour 2 inches of vegetable oil into a deep skillet or heavy-bottomed pot and heat to 350°F.
04 - Carefully lower the egg rolls into the hot oil in small 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 - Combine the granulated sugar and cinnamon in a shallow dish. Roll each warm egg roll in the cinnamon sugar mixture until evenly coated on all sides.
06 - Serve the egg rolls warm, optionally accompanied by a scoop of vanilla ice cream.