To prepare the chicken: The day before serving, season the chicken legs well with salt and pepper. Refrigerate overnight.
The next day, preheat the oven to 350 degrees F. Saute the carrot, celery, and onion in the butter and oil. Caramelize lightly, then deglaze the pan with the brandy. Transfer to the bottom of an ovenproof pan that will just hold the chicken legs. Arrange the legs skin side up. Add the bay leaves, garlic, peppercorns, and chicken stock. The bottom half of the meat should be immersed in the liquid, but the skin should be exposed. Braise on the top rack of the oven, checking after 45 minutes, until the meat is tender and the skin crispy.
Before serving, pour off some of the braising liquid with the vegetables. Degrease the liquid and reduce by a third. Taste as it is reducing to ensure that the salt doesn't intensify too much. If it is too salty, add a little plain reduced stock. Finish with the parsley.
To prepare the greens: Lightly brown the onion in the oil and the butter. Chop the greens into manageable pieces and saute slowly until wilted. Add a little water to prevent sticking if necessary. When the greens are cooked through, add the anchovy and garlic and cook a minute more. Turn off the heat and season with salt, pepper, cayenne, and lemon juice.
Serve the braised chicken with the greens.
Recipe courtesy of "Bay Wolf Restaurant Cookbook" (10 Speed Press, 2001) by Michael Wild and Lauren Lyle