Preheat the Smoker: Set your smoker to 225°F to 250°F. Use a mild fruitwood like apple or cherry, which pairs beautifully with the natural sweetness of the squash.
Prep the Veggies: Score the flesh of the squash halves in a diamond pattern. Drizzle the squash, onion quarters, carrot chunks, and the exposed head of garlic with olive oil, then season lightly with salt and pepper.
Smoke: Place all the vegetables directly on the smoker grates (or use a parchment-lined wire rack for the smaller pieces). Smoke for 1.5 to 2 hours until the squash is completely fork-tender.
Assemble: Let the veggies cool slightly. Scoop the soft smoky squash flesh out of its skin. Squeeze the roasted garlic cloves right out of their papery skins.
Blend and Simmer: Transfer the squash, garlic, onions, and carrots to a high-powered blender or a large soup pot if using an immersion blender. Add the stock, honey, and fresh thyme. Blend until completely smooth.
Finish: Warm the soup through over medium-low heat. Stir in the heavy cream if you prefer a richer texture, and adjust your salt and pepper to taste.
