Cook noodles per package instructions.
Heat peanut oil in a pan or wok over high heat.
Add chicken and cook until browned, then season lightly with salt and pepper.
Remove chicken and set aside.
Prepare the sauce by mixing all ingredients together in a small bowl.
Set sauce aside.
Add shredded cabbage and carrot to the same pan and stir-fry for 1 ½ minutes until the cabbage is mostly wilted.
Return chicken and noodles to the pan, pour in the sauce, and stir well.
Cook for an additional 2-3 minutes until the chicken is heated through and the sauce has thickened.
