In a Dutch oven or large kettle, bring 6 cups water to a boil. Add the pearl onions; boil for 3 minutes. Drain and rinse with cold water; peel.
In a large roasting pan, combine the onions, potatoes, rutabaga, parsnips and carrots. Drizzle with butter and oil. Sprinkle with thyme, salt and pepper; toss to coat.
Cover and bake at 425° for 30 minutes.
Uncover; stir in Brussels sprouts and garlic.
Bake, uncovered, for 50-60 minutes or until vegetables are tender and begin to brown, stirring occasionally.
