In a large saucepan, heat the olive oil until shimmering. Add the celery, carrot and onion and cook over moderate heat, stirring, until lightly browned, about 10 minutes. Add the anchos and cook until fragrant, about 2 minutes. Add the stock, ketchup, vinegar, molasses, sugar and dry mustard and simmer over moderate heat until the barbecue sauce is reduced to about 3 cups, about 30 minutes.
Transfer the mixture to a blender and puree until smooth. Return the sauce to the saucepan and simmer until thickened and reduced to 23/4 cups, about 5 minutes longer. Season with salt.
Light a grill. Cut in between the bones to separate the rack into individual ribs. Grill the ribs over moderate heat, turning, until crusty and sizzling, about 10 minutes. Brush generously with the barbecue sauce and grill, turning, until deeply glazed, about 5 minutes longer. Serve the ribs, passing the extra sauce on the side.
ABOUT THIS RECIPE
These beef ribs—leftovers from the giant rib roast—are incredibly luscious. I douse them in sweet and tangy homemade barbecue sauce, then cook them on the grill until they’re crusty, sizzling and outrageously good.