Soak the mussels in water, then scrub any dirt or grit from the shells. If mussels are not de-bearded, remove the beard with a sharp knife. Set aside.
In a deep, wide pan, sauté the onions in butter over medium heat.
Once onions are fragrant and translucent, add the mussels, beer and stock. Cover with a lid and cook, shaking the pot frequently. Check the mussels after two minutes, and often, removing them to a serving bowl once the shells open. Discard any mussels that do not open.
Boil the stock and beer until it reduces to a sauce-like consistency; a few minutes. (Keep the mussels covered to preserve their warmth.) Stir in the heavy cream and remove the sauce from the heat. Taste, and season well with salt and pepper.
Divide the mussels evenly among two bowls and pour over sauce. Top with fennel fronds, and eat with toasted, buttered bread.