1. Preheat oven to 325°F (165°C).
2. Heat olive oil in a Dutch oven over medium-high heat. Brown lamb shanks on all sides. Remove and set aside.
3. In the same pot, add carrots, celery, and onion. Cook until softened, about 5 minutes.
4. Add garlic and cook for another minute.
5. Pour in white wine, scraping up any browned bits from the bottom of the pot. Let it reduce by half.
6. Add chicken broth, diced tomatoes, thyme, rosemary, salt, and pepper. Stir to combine.
7. Return lamb shanks to the pot. Bring to a simmer, then cover and transfer to the preheated oven.
8. Cook for 2 hours, or until the meat is tender and falling off the bone.
9. Garnish with fresh parsley before serving.