In medium sauce pan over medium heat, warm 1 tablespoon canola oil. Add ginger, carrot, fennel, garlic and shallot; cook, stirring, for 10 minutes. Add Mirin and continue cooking, stirring, about 5 minutes, or until reduced by 1 half. Add 2 cups chicken stock and lime zest; reduce heat to low and simmer 7 minutes. Strain broth through fine strainer, separating carrot mixture and reserving broth.
While broth is cooking, pound chicken breast halves to even thickness. Season both sides with salt and white pepper. In large sauté pan over medium heat, warm remaining tablespoon canola oil and butter. Add chicken and cook, turning, until golden brown and cooked throughout, about 6 minutes per side. Remove chicken and set aside.
Place bok choy and jicama in deep sauce pan. Add remaining ¾ cup chicken stock and cook over medium heat about 3 – 5 minutes, or until vegetables are tender but still have slight crunch left in stalks.
To serve, place bok choy and jicama mixture in center of plate. Top with chicken breast half. Spoon carrot mixture on top and pour ¼ of liquid broth over each chicken piece.