1. Preheat the oven to 350°F.
2. In a pan, heat the butter. Add the onion and cook for 3 minutes. Add the apples and pepper. Let the apples cook for about 3 minutes.
3. In a saucepan with a little water, place the cleaned mussels and cover. Cook for 6 minutes or until all the mussels are open.
4. Remove the mussels from their shells, keeping one side of the shell and the mussel inside.
5. Pour a little oil into a baking dish. Place the mussels, shell side down.
6. Crumble the blue cheese and garnish each shell with a piece.
7. Place some of the cooked apples in each shell.
8. Bake for 5 minutes to melt the blue cheese.
9. Remove from the oven and serve immediately.