Prepare the Filling: In a large skillet or wok, heat a tablespoon of vegetable oil over medium-high heat. Add the ground chicken and cook until browned, breaking it up with a spoon. Drain off any excess grease.
Add the Vegetables: Add the shredded cabbage, carrots, celery, and green onions to the skillet. Cook for about 5-7 minutes, until the vegetables are tender-crisp.
Season the Filling: Stir in the minced garlic, ginger, soy sauce, oyster sauce (if using), sesame oil, salt, and pepper. Cook for another minute, until everything is well combined and fragrant. Remove from heat and let the filling cool slightly.
Wrap the Egg Rolls: Place an egg roll wrapper on a clean surface with one corner pointing towards you (like a diamond). Spoon about 2-3 tablespoons of the filling onto the center of the wrapper.
Fold the Wrapper: Fold the bottom corner up over the filling. Then, fold in the two side corners, like you're making an envelope.
Roll it Up: Tightly roll the wrapper up from the bottom, tucking in the sides as you go. Before you seal it completely, lightly moisten the top corner with a little water or a beaten egg (this helps it stick). Finish rolling it up tightly.
Fry the Egg Rolls: Heat about 2 inches of vegetable oil in a large pot or deep fryer to 350°F (175°C). Fry for about 2-3 minutes per side, until golden brown and crispy.
Drain and Serve: Remove the egg rolls from the oil and place them on a plate lined with paper towels to drain. Serve hot with your favorite dipping sauces.