1. Scrub the potatoes and make shallow cuts around their middles to make it easier to cut them in half after baking. Bake the potatoes at 400 degrees until soft, about 1 hour, depending on the size of the potatoes.
2. Meanwhile, cut the ends from the stalks of broccoli and peel some of the outer skin off to make the stems more edible. Steam the broccoli until crunchy-tender and bright green. Drain and chop fine.
3. Cut potatoes in half and scoop out the insides into a bowl. Add the salt, olive oil and just enough milk to allow you to mash the potatoes into a smooth paste. Add the Parmesan cheese and the chopped broccoli and mix well.
4. Pile the mixture back into the potato shells, arrange on a baking dish and heat them to desired temperature.