Roast the garlic (optional but worth it). Preheat the oven to 400°F (200°C). Slice the top off a whole head of garlic, drizzle it with olive oil, and wrap it in foil. Roast for about 30 minutes, until the cloves are soft. Let it cool, then squeeze out the cloves.
Cook the aromatics. Heat the butter and olive oil in a large Dutch oven over medium heat. Add the diced onion and cook for about 5 minutes, until translucent. Add the roasted garlic, thyme, and chopped sage, and cook 1 more minute until fragrant.
Brown the mushrooms. Set aside 1½ cups of the sliced mushrooms for the garnish. Add the remaining mushrooms to the pot. Cook for 10 to 12 minutes, stirring occasionally, until they are deeply browned and most of their liquid has cooked off.
Simmer. Add the chopped carrots, stock, and white miso. Bring to a gentle boil, then reduce the heat and simmer for 20 minutes, until the carrots are completely soft.
Blend. Using an immersion blender, or working carefully in batches in a countertop blender, blend the soup until completely smooth. Return it to the pot.
Add the cream. Stir in the heavy cream and warm gently for 3 to 4 minutes. Do not let the soup boil after adding the cream. Taste and season with salt and black pepper.
Make the garnish. Meanwhile, sauté the reserved mushrooms in a little butter over medium-high heat until golden and caramelized. Season lightly with salt and pepper. For crispy sage, fry a few whole leaves in the same pan for 20 to 30 seconds, then drain on a paper towel.
Serve. Ladle the soup into bowls. Top with the sautéed mushrooms, crispy sage leaves, and freshly cracked black pepper. Finish with a light drizzle of truffle-infused olive oil and serve warm.
