Mix the finely chopped garlic, shallots, and parsley with the soft butter. Season with freshly ground pepper and sea salt.
Heat the white wine in a large pot over medium-high heat. Add the mussels and cook for 3 minutes until they open. Discard any mussels that don't open. Remove the opened mussels and discard the top shell of each one.
Arrange the mussel shells on a baking sheet. Spoon the garlic butter into each shell. Bake at 200°C (392°F) for 5-8 minutes until the butter is light brown.
Arrange the prepared mussels in circles on serving plates. Garnish with fresh parsley and mild chilli peppers. Serve with baguette.