Step 1: Prepare for Roasting: Preheat the oven to 425°F (220°C). Line a baking sheet with parchment paper. Cut the butternut squash in half lengthwise and scoop out the seeds. Cut carrots into 2-inch pieces, and quarter the onion. Toss the vegetables with oil, salt, and pepper. Keep the head of garlic whole. Trim off the top, place in aluminum foil, drizzle with a small amount of oil, and a pinch of salt. Fold the aluminum foil into a tight packet around the head of garlic. Arrange butternut squash, carrots, onion, and garlic on the prepared baking sheets in a single layer.
Step 2: Roast: Roast for 35-40 minutes, stirring once halfway through, until vegetables are tender and lightly caramelized.
Step 3: Combine: Add roasted vegetables to the pot with broth, squeeze the roasted garlic cloves from their husks into the soup, and add all seasonings. Bring to a simmer over medium-high heat for 10 minutes.
Step 4: Brown the Butter: While the vegetables simmer, in a small saucepan, melt butter over medium heat. Continue cooking, stirring with a wooden spoon, whisk, or rubber spatula, until the butter foams, turns golden brown, and smells nutty, about 5-8 minutes. Remove from heat immediately and set aside.
Step 5: Blend the Soup: Pour in the browned butter and cream (or coconut milk). Using an immersion blender, blend until completely smooth. Alternatively, blend in batches in a regular blender, being careful with hot liquids. A high-powered blender will generally achieve a more velvety texture than an immersion blender.
Soup pureed in a white Dutch oven. An immersion blender on the countertop.
Step 6: Season and Finish: Add more broth if needed to reach the desired consistency. The soup should be creamy but not too thick. Season with salt and pepper to taste.