Preheat your oven to 400°F (200°C).
Wash and scrub the potatoes thoroughly, then prick each one with a fork.
Place the potatoes directly on the oven rack and bake for 45-60 minutes, until fork-tender.
While the potatoes bake, steam the broccoli florets until tender, about 5-7 minutes.
Once baked, remove the potatoes from the oven and allow them to cool slightly.
Slice each potato in half lengthwise and scoop out the insides into a mixing bowl, leaving a thin layer of potato in the skin.
Add the steamed broccoli, shredded cheddar cheese, sour cream, green onions, butter, salt, and pepper to the potato flesh in the bowl.
Mash the mixture until smooth and well-combined, then taste and adjust the seasoning if necessary.
Spoon the broccoli and cheese mixture back into the potato skins, mounding it on top.
Sprinkle any remaining cheddar cheese on top of the filled potatoes and return them to the oven.
Bake for an additional 15-20 minutes, until the tops are golden and the cheese is melted.