Make the Egg Rolls: Mix carrot, cabbage, soy sauce, and rice wine vinegar in a bowl. Season with salt and pepper.

Lay out an egg roll wrapper in a diamond shape. Add filling across the middle. Moisten edges with water. Fold and roll tightly, sealing any tears with an extra wrapper if needed. Repeat for the remaining wrappers.

Fry the Egg Rolls: Heat canola oil in a saucepan over medium heat to 325°F (163°C).

Carefully fry egg rolls in batches until golden brown. Drain on paper towels.

Prepare Chow Mein Noodles: Cook noodles in salted boiling water per package instructions. Drain and set aside.

Make the Sauce: Mix soy sauce, oyster sauce, sesame oil, sugar, and black pepper in a small bowl. Set aside.

Stir-Fry the Chicken and Vegetables: Heat vegetable oil in a wok over high heat. Stir-fry chicken until browned and cooked through. Remove and set aside.

In the same wok, heat the remaining oil. Stir-fry onion, bell pepper, carrot, cabbage, and garlic for 2-3 minutes until crisp-tender.

Combine Chow Mein: Add cooked chicken back to the pan and pour the sauce mixture over the chicken and vegetables. Stir to coat.

Add cooked chow mein noodles and toss well. Cook for 2-3 more minutes until heated through. Remove from heat. Garnish with scallions.

Prepare Coconut Lime Water: Mix coconut water with lime wedges.