Season legs and thighs with pepper, heat olive oil and butter on medium-high in a frying pan and brown the legs, about 3 minutes each side.
Place the legs and thighs and chicken broth in a crockpot. Add water to ensure all portions of the meat are covered with liquid. Cook on high for 4 to 6 hours, or until the meat is tender (time varies depending on the size of the geese).
Combine honey, rice vinegar, soy sauce, chili sauce, garlic, and ginger in a saucepan over medium heat. Bring to a gentle boil. Reduce heat and simmer for several minutes until it thickens.
Gently remove the legs from the crockpot and place them in a shallow pan. Pour half of the sauce over the goose, and let it marinate for 10 minutes. Place the legs and thighs on a serving plate, and cover with the remaining sauce. Serve immediately.