Cook the Filling:
In a large skillet or wok, heat 1 tablespoon of vegetable oil over medium heat. Add the ground pork or chicken and cook, breaking it apart with a spatula, until browned and fully cooked.
Add Vegetables:
To the cooked meat, add the shredded cabbage, carrots, soy sauce, oyster sauce, sesame oil, garlic powder, ginger, and black pepper. Stir-fry for 3–5 minutes until the vegetables are tender and the mixture is well combined. Stir in the sliced green onions and remove the skillet from the heat. Let the filling cool to room temperature.
Prepare the Egg Rolls:
Place an egg roll wrapper on a flat surface with one corner facing you. Add about 2-3 tablespoons of the cooled filling in the center. Fold the bottom corner over the filling, then fold in the two side corners. Brush the top corner with a little beaten egg and roll the wrapper tightly to seal the egg roll. Repeat this step with the remaining wrappers and filling.
Fry the Egg Rolls:
Heat about 2 inches of vegetable oil in a frying pan or deep fryer to 350°F (175°C). Carefully add the egg rolls, a few at a time, to the hot oil. Fry for 3–5 minutes or until they are golden brown and crispy, turning occasionally to ensure even cooking.
Drain and Serve:
Remove the egg rolls from the oil and place them on paper towels to drain excess oil. Serve hot with sweet and sour sauce or soy sauce for dipping.