Peel and finely chop the onion and potato. Trim and peel the carrots and finely chop them.
Warm a pan for 1 min, then add 1 tbsp oil and the chopped veg. Add 1 star anise and season with salt and pepper. Cover and set the heat to low. Sweat for 10 mins, stirring now and then, till the veg are soft.
Crumble in the stock cube and add 800ml boiling water (or use hot homemade stock). Cover, bring to the boil and simmer for 20 mins till the veg are very tender.
Fish the star anise out of the pan. Ladle the soup into a blender and blitz till smooth, or use a hand-held blender in the pan. Taste the soup and add more salt and pepper if it needs it. Ladle into warm bowls and top with dill sprigs to serve.