Prepare the Sauce:

• Sweat the Aromatics: Heat a large saucepan over medium heat. Add olive oil and sweat the diced onion, garlic, thyme, and bay leaf until soft and translucent, about 5 minutes. Do not brown them.
• Tomato Paste: Stir in the tomato paste and cook for an additional 2-3 minutes until it deepens in color.
• Wine and Tomato Puree: Pour in the white wine and reduce by two-thirds. Add the tomato puree and simmer over medium heat, stirring occasionally for about 30 minutes, until thickened.
• Season and Finish: Season with salt and pepper, then stir in the olive oil. Let it cool slightly before refrigerating until needed.

2. Cook the Lamb:

• Preheat Oven: Set the oven to 325°F (165°C).
• Brown the Lamb: In a large oven-safe pot or Dutch oven, heat olive oil over medium-high heat. Season the lamb shanks generously with salt and pepper. Sear them until browned on all sides.
• Add Aromatics: Add bay leaves, garlic, onion, and carrot to the pot. Pour in chicken stock, ensuring the lamb is mostly submerged.
• Braise: Cover tightly with foil or a lid and place in the oven. Braise for 2 1/2 to 3 hours until the lamb is tender and falling off the bone.
• Cool and Shred: Remove from the oven and let the lamb cool in the cooking liquid. Once cool, shred the meat and discard the bones.
• Strain and Reduce: Strain the braising liquid and mix it into the tomato sauce. Simmer the combined sauce over medium-low heat for another 15-20 minutes to let the flavors meld.

3. Cook the Pasta:

• Boil Pasta: Cook the pasta in a large pot of salted water according to the package instructions, until al dente. Drain and reserve a bit of pasta water.
• Combine: Toss the pasta with the lamb ragu sauce. If the sauce is too thick, add a little pasta water to loosen it to your desired consistency.

4. Assemble and Serve:

• Serve: Plate the pasta and lamb ragu, garnishing with fresh basil leaves and shaved Parmesan cheese.