Place potatoes and garlic in a medium saucepan and pour over enough water to cover. Set pan over high heat and bring to a boil. Cook 8 minutes, until potatoes are fork-tender. Drain and return potatoes and garlic to pan. Add sour cream and mash until almost smooth (or lumpy if desired). Stir in parsley and season, to taste, with salt and black pepper.
Meanwhile, heat oil in a large skillet over medium-high heat. Season pork with salt and black pepper and add to hot pan. Cook 2 minutes per side, until golden brown. Remove pork from pan and set aside. To the same pan, add shallots and cook 2 minutes, until soft. Add thyme and tarragon and cook 1 minute, until fragrant. Add sparkling wine and cook 1 minute. Whisk flour into milk and add to pan. Return pork to pan and simmer 3 to 5 minutes, until pork is cooked through and sauce thickens. Serve 4 pork chops with all of the sauce and mashed potatoes. Reserve remaining pork for rice.