Add remaining 2 tablespoons oil to skillet, then stir in mushrooms and green onion whites. Cook over medium-high heat 5 to 7 minutes, stirring frequently, until softened. Stir in broth, carrots, cabbage, oyster sauce, soy sauce and ginger. Heat to boiling over high heat. Stir in chicken and spaghetti; return to simmering, then reduce heat and simmer uncovered 14 to 16 minutes, stirring frequently, until spaghetti is cooked through and sauce is thickened.