Combine the Sunbutter, fish sauce, lime juice, honey (or agave) red pepper flakes and water in a small saucepan and bring to a boil, stirring until smooth. Remove from the heat and set aside.
Heat the oil in a large skillet with a lid over medium-high heat. Add the garlic and ginger and toss in the oil for about 15 seconds. Add the chicken pieces and cook, stirring frequently, until browned on all sides, about 8 minutes. Add the broccoli, stir to coat, cover the pan and reduce the heat to medium. Cook until the broccoli is crisp tender and the chicken is cooked through – about 3 more minutes.
Add about ¼ of the Sunbutter sauce to the chicken and broccoli, toss to coat, place in a serving dish and sprinkle with sesame seeds if desired. Serve the rest of the sauce on the side.