Method for Chicken: Place chicken in medium bowl. Add oyster sauce, soy sauce, vegetable oil, and sugar and let marinade for 15 minutes. Cook chicken in boiling water for just a minute or two, drain and set aside.
Method for Sauce: In mortar and pestle, pound peanut until very fine and smooth. Set aside. In a wok, heat coconut milk. Keep stirring until coconut oil comes up to the surface, then add red curry paste. Cook until fragrant. Add more coconut milk if you prefer. Season with sugar, tamarind and fish sauce. Add peanut, stir until combined, and let it all cook for a few minutes longer. Remove from heat.
Final Preparation and Serving: Cook broccoli in boiling water for 1.5 minutes. Immediately transfer to ice cold water. THis stops the cooking process. Drain and place cooked broccoli on serving plate. Next put the cooked chicken over the broccoli. Pour peanut sauce over the chicken. Enjoy with fresh steamed jasmine rice.