In a food processor, add the deveined shrimp, and blend until it becomes a paste. Followed by the carrot, ginger, sesame oil, salt, and white pepper. Mix well.
Place the filling in a pastry bag (or a Ziploc bag), and cut open the tip.
Lay an egg roll wrapper flat with a corner pointing toward you, so that it looks like a diamond. Squeeze the filling in the bottom corner horizontally.
Fold the bottom corner up, followed by two sides toward the center. Continue to roll it up, until the top of the wrapper is left, and brush the beaten egg over it. Roll it up all the way. Repeat with the rest.
In a large pot over high heat, pour the oil inside. Heat it to 350 degrees F or 177 degrees C.
Transfer the shrimp egg rolls inside. Deep fry until crispy for about 4 minutes. Remove and drain.
