Heat oven to 325 degrees.
In a Dutch oven or ovenproof skillet with a tight-fitting cover, heat 1 tablespoon olive oil and brown the lamb shanks over medium heat. Sprinkle with salt and pepper, turning once after 5 minutes and cooking another 5 minutes. Transfer shanks to a plate.
Add 2 tablespoons olive oil to the pan drippings, and sauté the shallots, onions and carrots over medium heat until onions are translucent, about 7 to 8 minutes.
Deglaze the pan with the bottle of wine, stirring and scraping up browned bits in the pan for 2 to 3 minutes. Add the crushed tomatoes, broth, oregano and thyme, stirring well for 1 to 2 minutes.
Return shanks to the Dutch oven, nestling them in the sauce, and cover with lid. Transfer to oven and cook until meat is ready to fall from the bone, about 2½ to 3 hours. Remove from oven and let rest for 10 minutes before serving. Garnish with parsley and lemon zest.