Cook the Beef Filling:
Heat sesame oil in a skillet over medium-high heat. Add ground beef and cook until browned. Drain excess fat if needed.
Add Flavor:
Stir in garlic, ginger, soy sauce, brown sugar, rice vinegar, and red pepper flakes. Simmer for 2–3 minutes until well combined.
Add Veggies:
Add carrots, cabbage, and green onions. Cook for 2–3 more minutes until slightly softened but still crisp. Remove from heat and let cool slightly.
Assemble Egg Rolls:
Lay an egg roll wrapper in a diamond shape. Place about 2 tablespoons of filling in the center. Fold bottom corner up, then sides in, and roll tightly. Seal the edge with beaten egg.
Fry:
Heat vegetable oil in a deep skillet or fryer to 350°F (175°C). Fry egg rolls in batches for 3–4 minutes until golden brown and crispy. Drain on paper towels.
Serve:
Serve hot with dipping sauce on the side.