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

Lay an egg roll wrapper on a clean, dry surface. Scoop about 2 tablespoons of the beef filling into the center, fold the bottom corner over, tuck in the sides, and roll tightly, sealing the edge with water.

In a skillet, heat about 1 inch of vegetable oil over medium heat. To test, drop a small piece of the wrapper into the oil; it should sizzle.

Carefully add a few dumpling rolls to the skillet, frying for about 3-4 minutes on each side until golden brown and crispy.

Remove rolls from the skillet, placing them on paper towels to drain excess oil. Allow to cool slightly before serving with your favorite dipping sauces.