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Combine all the vegetables (except for the garlic) in a large roasting pan.
Cut about 1/2-inch off the top of the garlic head. Place on a square of aluminum foil, drizzle with 1 tablespoon of the olive oil, and loosely twist the top of the foil to enclose the garlic. Put in the pan with the other vegetables.
Drizzle the remaining 2 tablespoons of olive oil over the vegetables. Add the thyme, sherry, and Vegetable Shake or salt and pepper to taste and mix gently.
When ready to cook, start the Traeger grill on Smoke with the lid open until the fire is established (4 to 5 minutes). Set the temperature to 400F and preheat, lid closed, for 10 to 15 minutes.
Roast the vegetables, stirring occasionally, until they are tender and beginning to brown, about 1 to 1-1/4 hours.
Unwrap the garlic and squeeze the softened garlic cloves onto the vegetables; stir to combine. Discard the papery garlic husks. Serve immediately. Note: While you can substitute red beets, they tend to bleed as they cook and will discolor the other vegetables.