Brown sauce: Combine the ingredients and set aside.
In a large skillet or wok, add 2 T of the oil. Let it heat up until sizzling. Carefully add the chicken and stir fry until chicken is partially cooked. Remove to a plate.
Add 2 T more of the oil to the skillet and let it heat up. Add the onions and garlic; stir fry for 2 minutes Add the broccoli and pepper and stir fry for 2 minutes. Add the chicken back to the wok and add a little bit of water -- close the lid of the skillet and steam cook, until veggies and chicken are almost cooked.
Add the cilantro and coconut milk and cook until heated through and chicken is cooked.