Prepare the Filling
In a medium saucepan over medium heat, combine the peaches, brown sugar, cinnamon, nutmeg, vanilla, and butter.
Cook for 5-7 minutes, stirring occasionally, until the peaches soften and the mixture starts to thicken.
Stir in the cornstarch slurry and cook for another 1-2 minutes until the mixture becomes glossy and thick. Remove from heat and let it cool.
Assemble the Egg Rolls
Lay an egg roll wrapper on a clean surface with a corner pointing toward you (diamond shape).
Spoon 1-2 tablespoons of the peach filling onto the center of the wrapper.
Fold the bottom corner over the filling, then fold in the sides, and roll tightly to form a log. Seal the edge with water.
Fry the Egg Rolls
Heat about 2 inches of oil in a frying pan to 350°F (175°C).
Fry the egg rolls in small batches for 2-3 minutes per side, or until golden brown.
Remove and drain on paper towels.
Garnish and Serve
Dust with powdered sugar or cinnamon sugar for an extra touch of sweetness. Serve warm, and enjoy!