Pierce potatoes several times with a fork, place on a baking sheet and cook for 1 hour (or until cooked through). Allow to cool briefly.
Slice off top 1/3 of each potato, setting aside for a different use. Use a spoon to carefully scoop the potato filling from the bottom halves into a large bowl while leaving the skins in tact.
Use a potato masher to break down the potatoes. Stir in the sour cream, broccoli, cheese, chives and salt.
Scoop the filling back into each potato. If desired, grate some additional cheddar cheese on top of each potato for presentation.
Bake the potatoes for an additional 10 minutes or until heated through.