1. Place parsnips and potato in a pot and cover with water. Bring to a boil and cook until tender, about 15 minutes. Drain; return vegetables to pot. Add milk and 2 tablespoons butter; season with salt and pepper. Mash until smooth and cover to keep warm.

2. Season pork with salt and pepper. Melt remaining 2 tablespoons butter in a large skillet over medium-high heat. Cook pork, turning twice, until brown in places, about 5 minutes. Transfer to a plate. Cook shallots with thyme in skillet until softened; transfer to plate with pork. Cook pears, stirring once, until golden in places, about 2 minutes. Return pork, shallots, thyme, and any accumulated juices to skillet. Add vinegar and broth; simmer until pork is just cooked through, 1 minute. Serve with pears and pan gravy over mash.