Preheat the oven to 350˚F (180˚C).
Pat the lamb shanks dry with paper towels. Season with ½ teaspoon salt and ½ teaspoon black pepper.
In a medium Dutch oven or pot (that lamb shanks can fit) over high heat, warm 1 tablespoon olive oil. Sear the lamb shanks on all sides, about 7 minutes. Transfer the shanks to a plate. Use a paper towel to soak up the grease in the pot.
In the same pot over medium low heat, add 1 tablespoon olive oil. Add onion and garlic, saute for 2 minutes. Add carrot and celery. Cook for 5 minutes. Stir in the tomato paste. Then pour in red wine, crushed tomatoes, chicken stock, thyme and bay leaf.
Return the lamb shanks back to the pot. Move the vegetable aside to give space for the lamb. The lamb should be mostly covered. Bring to a simmer. Cover with a lid and transfer to oven. Cook for 2 hours 15 minutes.
Remove the lid and check the meat. The meat should be tender, but not falling off the bones yet. Cook uncover for another 15 minutes in the oven. Place the pot on stovetop. Transfer the shanks to a large plate. Cover with aluminum foil and keep warm.
Bring a medium pot of water to a boil. Add rice cakes and cook for 8 - 10 minutes. Drain and set aside.
Strain the sauce into a medium bowl through a sieve. Use the back of a spoon to squeeze out as much sauce as possible. Discard the vegetables. Return the sauce to the pot. Cook over medium-low heat for 2 minutes. Taste and adjust with salt and pepper to your own taste. Add rice cakes and cook for 3 more minutes.
Place the lamb shanks and rice cakes to serving plates. Top with more sauce and sprinkle with parmesan cheese if using. Serve immediately.