Discard any cracked or open mussels that do not close when tapped.
Heat half the butter and oil in a lidded pan and sauté shallots, wine, and mussels.
Steam for 3 minutes until mussels open, then drain and reserve the cooking liquid.
Sauté shallots in butter and oil, add mussel liquor and wine, and reduce by half.
Add courgette and tomatoes and cook for 2 minutes.
Stir in cream and saffron, simmer for 2 minutes, then add mussels and chervil.
Blanch samphire and sea aster in boiling water, then drain.
Fry the samphire and sea aster in butter for a few minutes.
Fry sea bass fillets skin-side down in butter and oil for 4 minutes until crispy.
Plate the sauce and vegetables, place the fish in the center, and garnish with greens.