In a skillet or wok over medium heat, add 1 tablespoon of vegetable oil. Add the garlic and ginger, sauté for 30 seconds until fragrant. Add the shrimp and cook for 2-3 minutes until just pink.

Add cabbage, carrot, and green onion. Stir-fry for another 2-3 minutes until vegetables are tender.

Stir in soy sauce, sesame oil, salt, and black pepper. Dissolve cornstarch in 1 tablespoon cold water, add to the skillet, and cook for 1 more minute until the mixture thickens. Remove the filling from heat and let it cool completely.

Lay an egg roll wrapper on a clean surface with a corner pointing towards you. Place 2-3 tablespoons of the cooled filling near the bottom corner. Fold the bottom corner over the filling, then fold in both sides and roll up tightly. Brush the top corner with beaten egg to seal. Repeat with all wrappers.

Heat the vegetable oil in a deep frying pan to 180°C/350°F. Carefully add egg rolls in batches. Fry for 2-3 minutes per side until golden brown and crisp. Remove with tongs and drain on paper towels.

Let cool slightly before serving. Enjoy with your favorite dipping sauce, such as sweet chili or soy sauce.