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