Toast anise seeds in a small frying pan over medium heat until fragrant, about 2 minutes. Transfer to a spice grinder and coarsely grind.
In a soup pot, melt butter over medium heat. Add onion and anise seeds and cook, stirring occasionally, until onion is soft, 7 to 10 minutes. Add carrots and cook, stirring occasionally, 10 minutes. Pour in stock, bring to a simmer, and cook until carrots are tender, about 15 minutes. Remove from heat.
In batches, purée soup in a blender until very smooth, 2 to 3 minutes per batch. Strain purée through a fine-mesh strainer into a pot and season with salt and pepper. Place over medium heat, stir in cream, and heat until hot. Stir in 4 tbsp. liqueur; season with salt and pepper.
In a bowl, stir together crème fraîche and remaining 1 tbsp. liqueur; season with salt. Ladle soup into warmed bowls. Drizzle with crème fraîche and sprinkle with chives.