Heat the oil in a large Dutch oven over medium heat. Add the lamb chunks and brown them on all sides for about 8 minutes.
Add the diced onion to the pot and cook until it softens, about 5 minutes.
Stir in the carrots, potatoes, and rutabaga. Cook for another 3 minutes while stirring.
Pour in the lamb broth, then add the salt and black pepper. Bring the mixture to a simmer.
Cover the pot and let it cook gently for 1 hour and 15 minutes, until the lamb is tender.
Stir in the chopped angelica leaves during the last 10 minutes of cooking. Taste and adjust salt if needed before serving.