Brown the beef in a skillet over medium-high heat until no pink remains, about 5 minutes. Drain all but 1 tbsp fat, then stir in the garlic and ginger and cook 30 seconds.

Add the cabbage, carrot, soy sauce, sesame oil, and pepper. Cook 3-4 minutes until the cabbage wilts. Spread the filling on a baking sheet to cool for 10 minutes.

Place a wrapper with a corner pointing toward you. Spoon about 2 tbsp filling across the middle. Fold the bottom corner up, fold in the sides, and roll tightly, sealing the top corner with water.

Heat 1 inch of oil in a deep pan to 350°F (175°C). Fry egg rolls in batches for 3-4 minutes, turning once, until golden and crisp. Drain on a rack or paper towels.

Slice a few diagonally to show the filling and serve hot with dipping sauce.