Prepare the filling: In a skillet, cook ground meat until browned. Add garlic, green onions, carrots, and cabbage. Cook until veggies soften. Stir in soy sauce, sesame oil, salt, and pepper. Remove from heat and let cool slightly.
Assemble the egg rolls: Place a wrapper on a flat surface with a corner pointing toward you. Add 2 tbsp of filling in the center. Fold the bottom corner up over the filling, then fold in the sides, and roll tightly. Seal the top corner with the beaten egg.
Fry the egg rolls: Heat oil in a pan (about 350°F / 175°C). Fry a few egg rolls at a time until golden brown and crispy, about 2–3 minutes per side. Drain on paper towels.
