Heat the oil in a large skillet or wok. Add the chicken pieces and cook until lightly browned.
Remove chicken from pan. Add garlic, ginger and carrot. Saute for 2 minutes.
Add remaining ingredients (except broccoli and corn starch).
Heat sauce over medium until well mixed and dissolved.
Add chicken back to pan and bring to a rapid boil. Reduce heat and simmer, covered, for ~20 minutes.
Add 2 Tbs water to cornstarch, mix to form a slurry.
Add cornstarch slurry and broccoli to pan, cover and simmer 3-5 minutes until heated through and sauce is thickened.
Serve over rice.
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