Preheat the oven to hot (Mk 7 - 425ºF - 220ºC). Scrub the potatoes to clean the skins then place them directly on the rack in the centre of the oven. Bake them for about 1 hour until they are easily pierced with a fork. Remove them from the oven and turn the oven down to moderately hot (Mk 6 - 400ºF - 200ºC).
Grate (shred) the cheese, then use a wad of kitchen paper or a towel to hold the potatoes (they are going to be hot!) and cut a slit along the top of each one. Using a spoon, carefully scoop out the flesh into a bowl, leaving the skins intact. Mash the potato lightly with a fork then add the butter, the sour cream, and half of the grated cheese. Add salt and freshly ground black pepper to taste then spoon the mixture back into the potato skins, mounding it slightly on the top.
Place the potatoes on a baking sheet, and bake for a further 15 to 20 minutes until completely heated through. Meanwhile, cut the broccoli into tiny florets and cook them in boiling water for 7-8 minutes until tender.
Gently press a few broccoli florets into the tops of each potato and sprinkle the remaining cheese over the top. Bake for a further 5-6 minutes until the cheese has melted. (If you are not vegetarian, you can finely chop a couple of rashers of bacon and add it to the cheese that you sprinkle over the top of each potato. It just adds a tang of sweetness.)