In a large mixing bowl, combine the ground beef, green onions, grated carrots, soy sauce, sesame oil, garlic, ginger, and red pepper flakes. Mix well until all ingredients are evenly incorporated.

Lay an egg roll wrapper on a clean surface with one corner pointing toward you. Place about 2 tablespoons of the beef mixture in the center of the wrapper. Fold the bottom corner over the filling, then fold in the sides, and roll tightly to seal. Repeat with remaining wrappers and filling.

Heat about 1 inch of vegetable oil in a large skillet over medium heat. Once the oil is hot, carefully add a few dumpling rolls at a time, frying until golden brown and crispy, about 3-4 minutes per side. Remove and drain on paper towels.

Serve hot with your favorite dipping sauce, such as sweet chili sauce or soy sauce.