Season chicken with salt and pepper. In a large skillet, cook chicken in hot oil over medium-high heat for 4 minutes. Turn chicken and add onion and ginger. Cook for 4 to 5 minutes more, stirring onions, until chicken is no longer pink (170 degrees F). Transfer chicken to a platter; keep warm.
Add broth and vinegar to skillet. Bring to boiling; boil gently, uncovered, for 5 minutes or until reduced by about half. Add apples and coleslaw mix. Cook and stir gently about 5 minutes or until apples and cabbage are just tender. Return chicken and any accumulated juices to skillet. Serve with orange wedges for squeezing over top.