Preheat oven to 385 degrees F.
Using a fork prick each potato several times then lightly coat with olive oil.
Bake potatoes 45 minutes to 1 hour, or until tender.
While potatoes are baking: Into a medium size skillet, add broccoli and 3 tablespoons water. Sauté 3 minutes, until broccoli is crisp tender. Drain and set aside.
Remove potatoes from oven. Leave the oven on.
Once the potatoes are cool enough to handle, slice each potato length-wise and remove tops.
Scoop out insides, leaving enough potato that the skin retains its shape.
Into a medium mixing bowl, add the scooped out potato and butter. Mash together until it reaches your desired consistency.
Fold in the broccoli, scallions, parsley, cheddar cheese, salt, and black pepper. Adjust seasoning to taste.
Spoon mixture back into the potato skins.
Return stuffed potatoes to the oven. Bake 15 minutes.
Garnish with a sprinkling of paprika.