For the lamb:
Position a rack in the center of the oven and preheat to 500 degrees 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 degrees 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 1/2 cup 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.