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For the lamb:
Position a rack in the center of the oven and preheat to 500° F. Trim the excess fat from the lamb, but leave a thin layer of at least 1/8 inch. Wipe dry and liberally rub it with salt and several generous grindings of black pepper, then pack the mint over the entire surface. Lightly butter the bottom of a roasting pan and put in the lamb, fat side up.

Roast in the center of the oven for 20 minutes, or until well-seared and lightly browned. Remove and pour the bourbon over it. Return it to the oven, reduce the heat to 375° F. and roast, basting occasionally with pan juices, until done to your taste, from 15 minutes per pound for medium-rare to 25 minutes per pound for medium well.

For the Madeira Pan Gravy:
Put the roasting pan over direct medium high heat. Add the Madeira and bring it to a boil, stirring and scraping the pan to loosen any cooking residue. Boil 1 minute and add the broth and pan juices. Bring to a vigorous boil and cook until reduced by about half, about 3 to 5 minutes.

Turn off the heat and swirl or whisk in the butter until it is incorporated. Taste and adjust the seasonings and pour into a warmed sauceboat.