Heat 2 tablespoons olive oil in a Dutch oven over medium-high heat until shimmering. Pat lamb shanks dry, season with salt and black pepper, then sear for 4-5 minutes per side until deeply browned. Remove shanks and set aside.
2 tablespoons olive oil, 4 pieces lamb shanks, salt, black pepper
Reduce heat to medium. Add chopped onion, carrots, and celery to the same pot. Cook for 5 minutes, stirring occasionally, until softened. Add minced garlic and tomato paste; stir constantly for 1 minute until paste darkens and raw flavor cooks out.
1 large onion, 2 pieces carrots, 2 stalks celery, 4 cloves garlic, 2 tablespoons tomato paste
Pour in red wine and scrape up the browned bits from the bottom with a wooden spoon. Add broth, fresh rosemary, and thyme, then return shanks to the pot. Ensure liquid reaches halfway up the meat; add more broth if necessary.
1.5 cups red wine, 2 cups beef broth, 3 sprigs fresh rosemary, 4 sprigs fresh thyme, 4 pieces lamb shanks
Cover the Dutch oven with the lid and transfer to a preheated oven at 325°F. Braise for 2.5 to 3 hours, checking liquid level at 90 minutes and adding broth if it drops below halfway. Shanks are done when meat pulls away from bone easily and internal temperature reaches 190°F.
4 pieces lamb shanks
Remove the pot from the oven and let the shanks rest, covered, for 10 minutes to redistribute juices. Skim excess fat from the surface if desired. Serve the shanks with sauce spooned over the top.