For the filling: Combine the shrimp, carrot, ginger, sesame oil, salt, and white pepper in a bowl.
For the egg rolls: Place an egg roll wrapper on a flat surface in a diamond shape. Place 2-3 tablespoons of the shrimp filling in the center of the wrapper. Fold the bottom corner over the filling, then fold in the sides and roll up tightly. Brush the top corner with the beaten egg to seal.
In a large pot or wok, heat 3 cups of oil to 350°F. Fry the egg rolls in batches for 2-3 minutes until golden brown. Drain on a paper towel-lined plate.
