In a medium saucepan, sauté the onion in 1 tbsp of butter until golden brown.

Add chicken stock and reduce it as far as you can without letting it going dry.

Add the cider, spices, and rum and bring to a boil.

Simmer at least 2 minutes--if you want to make the sauce richer, reduce it a bit.

Add the remaining 3 tbsp butter and remove the sauce from the heat when the butter has melted.

Boil enough water to cover the mussels. Plunge the the mussels into the water for one minute and drain.

Place the mussels in a serving dish and pour the cider mixture over them.