Preheat oven to 350° Oil a 6 to 8 cup shallow baking dish.
Pierce sweetpotato skins. Microwave until tender, about 4 to 6 minutes; cool.
In large skillet, heat oil over medium heat. Add onion and celery; cook and stir until tender, about 5 minutes. Add garlic; cook and stir 1 minute.
Add beef; cook and stir until it just begins to brown.
Stir in tomato sauce, Worcestershire, 1 teaspoon of the thyme and 1/4 teaspoon of the salt and pepper; bring to a boil. Transfer to baking dish, spreading evenly.
Scoop sweetpotato from skins into medium bowl. Add butter, milk, remaining ½ teaspoon thyme and ¼ teaspoon each salt and pepper. With electric beater, beat until smooth. Spread over meat in baking dish.
Bake until bubbly, about 20 to 25 minutes.