Crush the unpeeled ginger and whole green onions and add them with the rabbit to a pot of boiling water. Simmer just until cooked, remove, and cool. Chop into bite-sized cubes.
Mash the black beans. Heat the oil (not the sesame or chili oil) until hot in a wok. Add the hot bean paste and black beans, and stir for a minute, until very red and fragrant. Mix with the remaining sauce ingredients.
Chop the white and green parts of the onions into bite-sized pieces. Combine the rabbit, green onions, peanuts, and sauce, and mix well.
If you want to serve this hot, add the remaining ingredients to the wok with the bean paste and black beans, then add the rabbit, onions, and peanuts. Stir just until hot, then serve.