In a small bowl, combine the brown sugar, salt, coffee, mustard, black pepper, cayenne and paprika.
Preheat the oven to 275F. Pour off any liquid on the baking sheets, cover the ribs with foil and roast for about 3 1/2-4 hours, until the meat is tender but not quite yet falling off the bone. Pour off any liquid on the baking sheets.
Meanwhile, in a saucepan, melt the butter. Add the onion, garlic and thyme and cook over moderate heat until the onion is softened, about 5 minutes. Add the ketchup, vinegar, beef broth, hot sauce, bourbon, Worcestershire sauce, and molasses, and bring to a boil. Simmer over low heat, stirring occasionally, until thickened, about 30 minutes.
You can also do this on the grill. Have it heated up to 400F or moderately hot. Grill the rack, basting and turning, till you have the crust you want!
MAKE AHEAD
The roasted ribs and barbecue sauce can be refrigerated separately for up to 4 days. Return to room temperature and broil just before serving.
This recipe calls for 4 racks of ribs. If you want to make just one or two racks, I would still suggest making the entire rub and sauce. You can always refrigerate or even freeze the unused portions.
Adapted from Food and Wine