Slash the sea bass skin and season the flesh with salt.
Fry the fish skin-side down in oil and butter for two minutes per side.
Sauté onion, garlic, and star anise in butter and oil for one minute.
Add mussels and wine, cover, and cook until shells open.
Remove mussels, add stock to the pan, and reduce by one third.
Blend reduced stock with two-thirds of the shelled mussels until smooth.
Return purée to the pan, add cream, and heat with remaining mussels.
Stir-fry courgette ribbons in butter and oil and season with salt and pepper.
Plate courgettes, top with fish, and pour soup around the edges.