Preheat your oven to 325°F (165°C).
Heat the olive oil in a large Dutch oven or oven-safe pot over medium heat.
Sear the beef shanks on both sides until browned, about 5 minutes per side. Remove from the pot and set aside.
Add the onion, garlic, carrots, and celery to the pot and sauté until the vegetables are softened, about 5-7 minutes.
Stir in the tomato paste, beef broth, bay leaves, thyme, salt, and black pepper.
Return the beef shanks to the pot and spoon some of the sauce over the top.
Cover the pot and transfer it to the preheated oven. Bake for 2-3 hours, or until the beef is tender and falling off the bone.
Remove from the oven and let the beef shanks rest for 10 minutes before serving.
Serve the beef shanks hot with the sauce and your favorite sides.