Heat oil and sugar together in a wok over medium heat, stirring frequently. Watch this very carefully, when the sugar caramelizes in little brown globs then add the chicken and roll it around in the caramel to coat.
Add the water, teriyaki sauce, 5 spice powder and salt. Bring to a boil. Reduce heat to low and simmer gently covered for 45-50 minutes, turning the chicken once or until it's tender but not falling off the bones. Turn off the heat and let the chicken sit in the sauce for 10 more minutes.
Carefully lift the chicken out of the liquid and transfer to a cutting board. Slice in small pieces in a rosette pattern. Clean off the bones and pile the meat in the middle of the chicken rosette. Surround the chicken with the cucumber and green onions if you like.
Add the sesame oil to the sauce and reduce over high heat until slightly thickened, about 6-8 minutes. Drizzle of the chicken and serve the rest on the side.
NOTE: You can braise a duck in the same way, but use 10 cups of water. and simmer the duck for 2 hours.