Beat together the butter, Amarula, chilli and lime juice. This can be done by hand or in a small food processor bowl, mixing until the butter is smooth.
Roll the butter into a log and wrap tightly in cling film or baking parchment. Place in the fridge for about 30 minutes to chill.
To cook the fish, over the bottom of a frying pan with a thin layer of the oil and heat until it is really hot. Season both sides of the sea bass with salt and place skin side down in the pan for about 2 minutes, for the skin to crisp. To prevent the fish from curling, lightly hold down with a fish slice or by placing a small ramekin dish on top.
Turn the fish over and cook for a further minute over the high heat, until golden and just cooked. Sit the fish onto plates and add a slice of the butter on top of each fillet straightaway so the butter melts over the top, with accompaniments of your choice.
The prepared butter can be stored in the fridge for up to 1 week, or in the freezer for up to a month.