Preheat the oven to 180C/355F/Gas 4.
Twist each of the pastry strips twice to form straw shapes and lay on baking parchment on a baking tray. Sprinkle with the grated cheese and bake in the preheated oven for 10 minutes, or until golden-brown. Remove from the tray and allow to cool.
To make the rouille, put the garlic, egg yolk, red chilli and saffron into a food processor and blend to a paste. With the motor running, slowly, pour enough oil to bring the mixture together to a thick mayonnaise-like consistency.
For the soup, melt the butter in a large saucepan and fry the onion, celery, garlic and fennel until soft, but not coloured. Stir in the flour and cook for two minutes. Add the tomato purée, pastis, white wine, fish stock, parsley and star anise. Simmer for one hour.
Add the fish to the pan and cook for five minutes, then remove the star anise and discard. Gently remove the fish from the stock and set aside.
Add the mussels to the hot stock and cover the pan. Cook for 5-10 minutes, or until the mussels are fully open and cooked through.
Stir the cream into the soup and return the fish to the stock. Season with salt and freshly ground black pepper, to taste.
Serve the soup in bowls at once with the rouille and gruyère straws.