Preheat oven to 350º F (180º C).
In a large oven-proof pot, heat oil over medium heat. Add meat and brown for about 10 minutes. Add onion, garlic, thyme, black pepper and mushrooms and cook until the onions are soft, about 10 minutes. Add chicken stock, turnip and carrots and bring to a boil. Cover and place in the oven for 30 minutes.
In a small bowl mix cold water (1 cup) and cornstarch (or arrowroot flour). Remove stew from the oven and stir in cornstarch mixture, sweet potatoes and potatoes. Cover and return to the oven for 30 minutes.
Remove the lid and cook for an additional 15 minutes. Serve.
This recipe makes great leftovers and can also be frozen.