Carbonara with Braised Lamb

Heat 2 tablespoons olive oil in a large skillet over medium-high. Sprinkle lamb with 2 ½ teaspoons salt and 1 teaspoon pepper. Cook until browned, about 3 minutes per side. Remove lamb from skillet. Add onions, carrots, and garlic; cook, stirring occasionally, until slightly softened, about 4 minutes. Add ½ cup dry red wine; cook, until mostly evaporated, about 3 minutes. Transfer mixture to a 6-quart slow-cooker. Stir in tomatoes, chicken broth, and cumin. Add lamb shanks, nestling into tomato mixture. Cover and cook on LOW until lamb is very tender, about 6 hours.

Transfer lamb shanks to a plate. Pour cooking mixture through a wire-mesh strainer into a bowl; discard solids. Reserve strained cooking liquid for another use, if desired. Shred lamb and set aside, covered.

Heat 1 tablespoon olive oil in a skillet over medium and cook pancetta until browned, about 3 minutes. Add sliced garlic cloves and crushed red pepper; cook until just starting to brown, 1 to 2 minutes. Whisk together whole egg and yolks, 1 1/2 oz. pecorino Romano cheese and Parmesan cheese, and 1/2 tsp. pepper in a large bowl.

Cook pasta in salted water according to package directions. Drain; reserving 3 Tbsp. pasta water. Add hot pasta and reserved pasta water to bowl with egg mixture. Toss until cheese is melted and yolks are thickened. Stir in pancetta mixture. Top pasta with 8 oz. shredded reserved lamb shank meat. Garnish with 1/2 oz. pecorino Romano cheese and chopped fresh flat-leaf parsley.