Prepare the filling: In a large skillet, heat a tablespoon of vegetable oil over medium heat. Add the ground pork or chicken and cook, breaking it apart with a spoon, until browned. Drain any excess fat.
Cook the vegetables: Add the shredded cabbage, carrots, garlic, ginger, and green onions to the skillet with the meat. Stir-fry for about 5-7 minutes until the vegetables soften.
Season the filling: Stir in the soy sauce, oyster sauce, sesame oil, salt, and pepper. Continue cooking for another 2-3 minutes. Remove from heat and allow the mixture to cool to room temperature.
Assemble the egg rolls: Lay an egg roll wrapper on a clean surface, with one corner facing you. Spoon about 2 tablespoons of the filling near the bottom corner. Fold the sides of the wrapper over the filling and then roll it up tightly, sealing the edge with a bit of water.
Fry the egg rolls: In a deep pan or wok, heat about 2 inches of vegetable oil over medium-high heat. Once the oil is hot (around 350°F or 175°C), carefully add the egg rolls in batches, frying them for 3-4 minutes until golden brown and crispy. Remove and drain on paper towels.
Serve: Serve your egg rolls hot with dipping sauce, such as sweet and sour sauce or soy sauce. Enjoy!