Preheat oven to 350 degrees F. Drizzle oil all over rib roast and season with salt and pepper. Lay rib roast, bone side down, in a large roasting pan. Spread mustard greens around the pan, then scatter the thyme and place the garlic bulb halves in the pan. Pour in apple juice and cider vinegar. Cover with aluminum foil and braise for 2 1/2 hours, basting every 30 minutes.

Remove the foil and baste the meat. Cook, uncovered, for 30 minutes more until the meat's surface caramelizes and the liquid reduces and forms a sticky glaze on the meat. Set ribs aside. Remove and discard thyme. Squeeze the garlic pulp into a blender along with the juices from the pan, and puree. Serve ribs over mustard greens with braising liquid and Velvety Mashed Potatoes.

In a small saucepan warm 1 cup heavy whipping cream and 4 tablespoons unsalted butter over medium heat until the butter melts; set aside. Peel 4 large Yukon gold potatoes; put in a medium saucepan and cover with cold water. Bring to a boil, then reduce the heat. Add 1 teaspoon kosher salt and simmer for 15 to 20 minutes, until the potatoes are very tender. Drain well. Pass the potatoes through a food mill or a ricer back into the saucepan. Stir in the warm cream and butter mixture until the cream is absorbed and the mixture is smooth. Stir in 1/4 cup extra-virgin olive oil. Season with kosher salt and pepper.