Combine the chopped garlic, chopped thyme, 1 tablespoon salt and 2 teaspoons pepper in a small bowl; stir in the olive oil to make a paste. Rub the garlic paste all over the rib roast and let sit at room temperature, 1 hour.
Preheat the oven to 450 degrees F. Scatter the smashed garlic cloves, thyme sprigs, carrots, celery and onion in a large roasting pan. Place the rib roast fat-side up on top of the vegetables. Pour 1 1/2 bottles stout into the bottom of the pan. Roast until the meat begins to brown and crisp on top, about 30 minutes.
Baste the meat with the pan juices and reduce the oven temperature to 300 degrees F. Continue to roast, basting with the pan juices every 30 minutes, until a thermometer inserted into the thickest part registers 115 degrees F to 120 degrees F for medium rare, 1 1/2 to 2 hours. Transfer to a platter or cutting board, tent with foil and let rest 30 minutes before carving.
Meanwhile, make the jus: Set the roasting pan over 2 burners and add the remaining 1/2 bottle stout and the beef broth. Bring to a boil and cook until reduced by about one-third, 6 to 8 minutes. Strain into a fat separator, discarding the vegetables. Pour the liquid into a saucepan, leaving any fat in the cup. Bring the liquid to a simmer, then whisk in the mustard. Cover and keep warm. To carve, position the roast so the bones are pointing up, then use a chef?s knife to remove the bones in one piece; thinly slice the meat against the grain. Serve with the jus.
Photograph by Ryan Liebe