Season the lamb shanks with salt and pepper. Heat olive oil in a large heavy pot over medium-high heat. In batches, brown the shanks on all sides, which should take about 8 minutes. Remove the shanks from the pot and set aside.

Add diced onions, carrot rounds, and minced garlic to the pot, and sauté until they turn golden, which will take around 10 minutes. Pour in the wine, diced tomatoes with their juice, chicken broth, and beef broth. Stir in the rosemary, thyme, and lemon zest.

Return the browned lamb shanks to the pot, ensuring they are mostly submerged in the liquid. Bring the mixture to a boil. Reduce the heat to medium-low, cover, and let it simmer until the meat becomes tender, approximately 2 hours.

Remove the lid and continue to simmer for an additional 30 minutes, or until the meat is very tender. (You can prepare this dish a day in advance. Allow it to cool, then refrigerate. Reheat over medium heat before serving.) Transfer the lamb shanks to a serving platter and cover with foil. Boil the remaining liquid in the pot until it reduces and thickens, about 15 minutes. Season with additional salt and pepper, then spoon the sauce over the lamb shanks before serving.