Heat 1 tablespoon canola oil in a large cast-iron skillet over medium-high. Add chicken; cook 5 minutes or until browned, stirring to crumble. Add mushrooms; cook 6 minutes, stirring occasionally. Remove chicken mixture from pan; keep warm.
Return pan to medium-high. Add remaining 1 tablespoon oil; swirl. Add bok choy; cook 3 to 4 minutes or until lightly browned, turning occasionally. Add green onions and ginger; sauté 2 minutes. Stir in chicken mixture.
Combine soy sauce, vinegar, and honey in a small bowl. Divide chicken mixture among 4 shallow bowls; top evenly with soy sauce mixture and peanuts.