Heat the oil in a large pot or Dutch oven over medium-high heat. Place the roast in the pot, and quickly brown on all sides.
Fill the pot with enough water to cover the roast. Add the onion, garlic, celery, basil, salt and pepper. Bring to a boil, then reduce heat to low and simmer for 2 hours and 15 minutes, adding water if needed to keep the roast covered. Add potatoes and turnips; simmer for an additional 15 minutes. Add carrots; simmer for 30 minutes, or until roast can be pulled apart with a fork. Taste, and adjust salt and pepper if needed before serving.
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