Prep the shanks. Pat your lamb shanks dry with paper towels and season generously with salt and pepper on all sides. Don't be shy with the seasoning – this is a big piece of meat! Tie each shank with kitchen twine if desired (keeps them from falling apart during cooking).
Brown the meat. Heat the olive oil in your Dutch oven over medium-high heat until it shimmers. Working in batches if necessary (don't crowd the pot!), sear the lamb shanks until deeply browned on all sides, about 3-4 minutes per side. This step is CRUCIAL for flavor – those brown bits are pure gold. Transfer the browned shanks to a plate and set aside.
Create the aromatic base. In the same pot with all those lovely meat drippings, add the onions, carrots, and celery. Cook for 5-7 minutes until they begin to soften. Add the garlic and cook for another minute until fragrant. Can you smell that? That's the smell of your neighbors getting jealous.
Build the braising liquid. Stir in the tomato paste and cook for 1-2 minutes until it darkens slightly. Pour in the red wine, scraping the bottom of the pot with a wooden spoon to release all those flavorful brown bits (aka fond, if you want to sound fancy). Let it simmer for 2-3 minutes to burn off some of the alcohol.
Return the shanks and add liquid. Add the stock, bay leaves, rosemary, and thyme to the pot. If using orange zest, add it now. Return the lamb shanks to the pot, arranging them so they're mostly submerged in the liquid. Bring to a simmer.
Low and slow magic time. Once simmering, reduce heat to low, cover the pot with a tight-fitting lid, and let cook for 2 to 2.5 hours. The shanks are done when the meat is tender enough to easily pull away from the bone with a fork. If you can twist the bone and it moves freely, you've hit the jackpot.
Finish the sauce. Remove the shanks and set aside, tented with foil to keep warm. Skim excess fat from the surface of the cooking liquid (or use a fat separator if you're fancy). If you'd like a thicker sauce, whisk flour with a little water to create a slurry, add to the pot, and simmer for 5 minutes. For extra richness, stir in a tablespoon of butter.
Serve like a pro. Place a lamb shank on each plate (over polenta, mashed potatoes, or with crusty bread if desired), spoon the vegetable-packed sauce generously over each shank, and sprinkle with fresh parsley. Prepare for the "oohs" and "aahs."