In a large mixing bowl, combine the shrimp, shredded cabbage, shredded carrots, green onions, minced garlic, soy sauce, sesame oil, salt, and pepper. Mix thoroughly until the ingredients are well combined.
Lay out one egg roll wrapper on a clean, flat surface, with one corner facing you. Place about 2-3 tablespoons of the shrimp mixture in the center of the wrapper.
Fold the bottom corner of the wrapper over the filling, then fold the two side corners towards the center. Roll the wrapper tightly from the bottom to the top to form a secure roll. Seal the edges with a little water if needed.
Repeat this process with the remaining wrappers and filling.
Heat the vegetable oil in a frying pan or deep fryer to 350°F (175°C).
Fry the egg rolls in batches for about 3-4 minutes or until golden brown, turning occasionally for even cooking.
Remove them and place on a baking sheet lined with paper towels to drain excess oil.
Serve the shrimp egg rolls hot, with sweet chili sauce or soy sauce for dipping.