- Melt butter in large saucepan over medium heat. Add leek and cook, covered, stirring occasionally, until softened, about 4 minutes. Add garlic and ginger and cook, stirring constantly, just until fragrant, about 30 seconds.
- Stir in carrots, parsnips, broth, star anise, salt, and pepper and bring to boil. Reduce heat and simmer, covered, until vegetables are very tender, about 40 minutes. Remove and discard star anise. Stir in half-and-half and let cool 5 minutes. Puree soup in blender in batches.
- Return soup to saucepan. Cook over medium heat, stirring occasionally, until heated through, about 2 minutes. Ladle soup evenly into 4 bowls and sprinkle with parsley.
- Per serving: 1 3/4 cups
Fragrant star anise has a distinctive licorice flavor that infuses the soup as it simmers. If you can't find it, you can substitute 1/4 teaspoon of five-spice powder or ground cinnamon.