Cut the ribs into individual bones if needed. Chop a few cloves of garlic and season the ribs with salt.
Place the ribs and garlic in a sealable bag with enough vinegar and a bit of water (1 part water to 2 parts vinegar) to coat the meat. Marinate for a few hours or overnight.
Remove ribs from the marinade, scrape off excess garlic, and place in a baking dish covered with foil.
Prepare garlic by cutting root ends, coating with oil, and wrapping in foil. Stab the potato a few times, coat in oil, and season with salt.
Put ribs, garlic, and potato in a 150°C oven. Cook until garlic is soft and golden brown (about 1 hour), ribs are very soft, and the potato is squishy (about 3 hours).
Pour out the liquid and rendered fat from the rib pan. Adjust seasoning if needed.
Cut the potato in half and scoop out the flesh. Mash the potato flesh with rib fat and rib broth until smooth. Squeeze roasted garlic into the mixture, and stir in cheese, salt, pepper, and thyme leaves. Stuff the potato skin with this mixture.
Mix 60 ml of barbecue sauce with molasses, mustard, soy sauce, hot sauce, and smoked paprika to taste.
Return ribs to the oven uncovered and turn the broiler on high. Brown the ribs on all sides under the broiler. Halfway through, return the potato to the oven to brown the top.
Brush a thin layer of BBQ sauce on the ribs and broil until the sauce is browned. Repeat with a second layer of sauce if desired.
Remove ribs and potato from the oven. Garnish ribs with fresh thyme leaves and serve with any additional BBQ sauce on the side.