In a large bowl, combine the shrimp, cabbage, carrots, green onions, garlic, ginger, soy sauce, and sesame oil. Mix well until all ingredients are evenly coated.
Lay an egg roll wrapper on a clean surface with one corner pointing towards you. Place about 2 tablespoons of the shrimp and cabbage 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 2 inches of vegetable oil in a deep skillet or pot over medium heat until hot (about 350°F).
Carefully add a few egg rolls at a time, frying for 3-4 minutes on each side or until golden brown and crispy. Remove and drain on paper towels.
Serve hot with your favorite dipping sauce.