Preheat your oven to 425°F (220°C). Toss the chopped root vegetables and whole garlic cloves with olive oil, making sure they are evenly coated. Spread them out in a single layer on a baking sheet.
Roast the vegetables and garlic in the oven until they are deeply caramelized at the edges and some pieces are slightly blackened, about 30-35 minutes. The garlic cloves should become soft and fragrant.
Once roasted, allow the vegetables to cool slightly. Peel the garlic cloves if you prefer a smoother soup, or leave them unpeeled for a more rustic texture.
Transfer the roasted vegetables and garlic to a large pot. Pour in the vegetable broth and bring to a gentle simmer over medium heat.
Add smoked paprika, salt, and black pepper to the simmering broth. Stir well to distribute the spices evenly and enhance the smoky flavor.
Use an immersion blender or transfer the contents to a blender in batches and blend until smooth and velvety. The soup should have a thick, creamy consistency with a warm, smoky hue.
Stir in the cream or coconut milk to enhance the soup’s richness and silkiness. Taste and adjust seasoning as needed.
Return the soup to low heat if needed, warm through, and serve hot. Garnish with a drizzle of cream or a sprinkle of smoked paprika if desired, and enjoy this smoky, comforting bowl.