01 - In a medium saucepan over medium heat, combine the diced peaches, granulated sugar, brown sugar, ground cinnamon, nutmeg, lemon juice, cornstarch, and a pinch of salt. Stir continuously until the mixture thickens and becomes glossy, approximately 5 to 7 minutes. Remove from heat and allow to cool slightly.
02 - Lay an egg roll wrapper flat on a clean work surface in a diamond orientation. Spoon approximately 2 heaping tablespoons of the peach filling onto the lower third of the wrapper. Fold the bottom corner up and over the filling, tuck both sides inward, and roll tightly toward the top corner. Brush the top edge with beaten egg to seal. Repeat with the remaining wrappers and filling.
03 - Pour vegetable oil to a depth of 2 inches into a deep skillet or heavy-bottomed pot. Heat the oil to 350°F over medium-high heat. Use a thermometer to monitor the temperature for consistent results.
04 - Carefully lower the assembled egg rolls into the hot oil in small batches. Fry for 2 to 3 minutes per side until golden brown and crispy. Transfer the finished egg rolls to a paper towel-lined plate to drain excess oil.
05 - Combine the granulated sugar and ground cinnamon in a shallow dish. While the egg rolls are still warm, roll each one through the cinnamon sugar mixture until evenly coated on all sides.
06 - Serve the peach cobbler egg rolls warm. Optionally accompany each portion with a scoop of vanilla ice cream.