For the ribs: Place the ribs in a roasting pan, cutting the racks in half to fit if necessary. Combine the garlic, rosemary, brown sugar, balsamic vinegar, salt and cayenne in a small bowl, and rub the mixture evenly all over the ribs. Allow the ribs to marinate in the refrigerator for at least 1 hour and up to 4 hours.
Place a rack in the center of the oven and preheat the oven to 425 degrees F. Pour 1/2 cup water into the roasting pan and cover the pan tightly with aluminum foil. Roast the ribs until the meat is very tender and separate easily from the bone, about 1 1/2 hours. While the ribs are roasting make the BBQ sauce.
For the sauce: Place the balsamic vinegar in a medium saucepan over medium-high heat. Bring to a boil then lower the heat to medium and cook the vinegar until it is reduced by a third, about 8 minutes. Whisk in the ketchup, apple cider vinegar, honey, mustard, molasses, Worcestershire, hot sauce and salt. Bring the the sauce back to a boil then lower the heat and simmer until thickened, 15 to 20 minutes, stirring occasionally. Remove from the heat and let cool to room temperature.
To finish, remove the ribs from the oven and transfer to 2 aluminum-foil-lined baking sheets. Increase the oven temperature to 450 degrees F. Brush both sides of the ribs generously with the BBQ sauce and bake uncovered for 10 minutes, until the sauce is browned and sizzling. Allow the ribs to rest for 10 minutes before slicing.