Boil the potatoes until almost done, then peel and chop them. Heat some oil in a wide, deep frying pan and add the cleaned mussels.
Wait for them to slightly open and sprinkle with salt and pepper. Add wine, put the lid on and wait for the shells to open fully. Take the mussels out from their shells.
Put the potatoes into a greased baking tin, add the mussels, blanch the broccoli florets briefly.
Add some wine sauce to the mussels, as well as oil and season well with salt and pepper. Leave the dish to bake for 15 minutes at a moderate oven heating.
Sprinkle with grated cheese and bake for another 5-10 minutes.