Begin by chopping the shrimp into small pieces. You can also leave some pieces whole for a varied texture if desired.
In a large mixing bowl, combine the chopped shrimp, shredded cabbage, grated carrots, chopped green onions, minced garlic, soy sauce, sesame oil, ground ginger, and a pinch of salt and pepper. Mix everything thoroughly until well combined.
Place an egg roll wrapper on a clean surface, with one corner pointing towards you. Spoon about 2 tablespoons of the shrimp filling onto the center of the wrapper.
Fold the bottom corner up over the filling, then fold in the side corners. Roll the wrapper tightly towards the top corner, sealing the edges with a little water if necessary. Repeat this process for all egg rolls.
In a wok or deep frying pan, heat enough vegetable oil to cover the bottom, about 2 inches deep, over medium-high heat. The oil is ready when it reaches 350°F (175°C).
Carefully place the egg rolls in the hot oil, a few at a time, being careful not to overcrowd the pan. Fry for about 3-4 minutes on each side, or until they turn golden brown and crispy.
Remove the egg rolls using a slotted spoon or tongs and place them on a paper towel-lined plate to drain any excess oil.
Serve hot with your favorite dipping sauce.