Melt butter in a large saucepan over medium-high heat. Add carrots, onion, garlic, and curry powder. Season with salt and pepper. Cook, stirring often, until carrots and onions are softened,10–15 minutes. Stir in broth, coconut milk, and chili sauce. Bring to a boil, reduce heat and simmer, stirring occasionally, until vegetables are completely soft and liquid is slightly reduced, 30–35 minutes. Let soup cool a bit, then purée until smooth using an immersion blender. Season with salt and pepper to taste. Serve topped with basil.