Prep the Lamb: Season and sear lamb chops in a Dutch oven until browned. Remove and set aside.
4 lamb shoulder chops, 2 tablespoons olive oil or lard, 1 teaspoon freshly cracked black pepper
Sauté Vegetables: Cook onions and carrots in the same pot until softened. Add tomato paste and cook until it becomes a rich dark red color. Add garlic and stir for 30 seconds until fragrant.
1 large onion, 3 cloves garlic, 2 large carrots, 2 tablespoons tomato paste
Deglaze and Simmer: Pour in red wine, scraping the pot to get all the browned flavorful bits at the bottom. Add herbs, vinegar, and stock. Bring to a simmer.
3 cloves garlic, 1 cup red wine, 1 cup beef or chicken stock, 1 teaspoon fresh rosemary, 2 sprigs fresh thyme, 1 bay leaf, 1 tablespoon balsamic vinegar
Braise: Return lamb to the pot and cover with lid. Simmer on low for 1.5–2 hours until tender. You can also do this step in the oven at 300°F.
Make Mashed Potatoes: Boil the potatoes in salted water until tender—about 25 minutes. Strain and then mash potatoes in the same, warm pot used for cooking with the warm milk, butter, sour cream, and mustards. Taste and add more salt if necessary.
2 teaspoons salt, 2 lbs Yukon Gold or Russet potatoes, 1/2 cup whole milk, 1/2 cup unsalted butter, 2 tablespoons sour cream, 1 tablespoon Dijon mustard, 1 teaspoon whole-grain mustard, 1/2 teaspoon salt
Serve: Check that lamb easily falls apart when tested with a simple fork. Remove bay leaf from braising liquid, adjust sauce seasoning, and serve lamb over mashed potatoes with sauce spooned on top.