Preheat oven to 300°F. Heat oil in a large roasting pan over medium-high. Season lamb with 1 tablespoon salt and 1 teaspoon pepper. Brown lamb in hot oil, 5 to 7 minutes on each side. Remove from pan. Add onion, carrot, and garlic cloves. Cook until slightly softened, 5 to 6 minutes. Add wine; cook 2 minutes, stirring and scraping bottom of pan. Stir in tomatoes and broth; cook 2 minutes. Return lamb to pan; bring to a boil. Place parchment paper directly on lamb; cover pan tightly with aluminum foil.
Bake in preheated oven 3 1/2 hours. Remove foil, and bake until meat falls off the bone or when a meat thermometer inserted in thickest portion registers 200°F, about 30 more minutes, turning halfway through.
Transfer lamb to a platter; cover with foil. Strain cooking liquid into a medium saucepan; discard solids. Add 1/2 teaspoon salt and 1/4 teaspoon pepper, and cook over medium-high until reduced to about 3 cups, 5 to 7 minutes. Spoon 1 cup sauce over lamb, and serve with remaining sauce. Top with parsley, and serve with Potato Hash.