Cook the ground pork in a skillet over medium-high heat for about 4 minutes until no pink remains. Add the garlic and ginger, stir for 30 seconds, then add the cabbage, carrots, green onions, soy sauce, sugar, and white pepper. Cook for 3 to 4 minutes until the cabbage is just wilted. Remove from heat, stir in the sesame oil, and spread the filling onto a plate to cool completely, at least 15 minutes.

Place a wrapper in a diamond shape, spoon 3 tbsp of filling across the lower third, fold the bottom corner up, tuck in the sides, roll tightly, then brush the top corner with beaten egg and seal. Repeat with all remaining wrappers.

Heat 2 to 3 inches of vegetable oil in a heavy pot to 350°F (175°C). Fry 3 to 4 egg rolls at a time for 3 to 4 minutes, turning once, until deep golden brown.

Transfer to a wire rack, rest for 2 minutes, then arrange on a serving plate with sliced green onions and dipping sauce alongside.