Preheat the oven to 385°F. Prick each potato several times with a fork, then lightly coat them with olive oil. Arrange the potatoes on a baking tray.  Bake in the preheated oven for 1 hour, or until the potatoes are fork tender. (The exact bake time may vary depending on the size of your potatoes.) Remove the potatoes and leave the oven on.

While the potatoes are baking, heat a medium skillet over medium-high heat. Add the finely chopped broccoli florets along with 3 tablespoons of water and sauté for about 3 minutes until the broccoli is crisp-tender. Once done, drain the broccoli and set it aside.

When the hot potatoes are cool enough to handle, use a sharp knife to slice off just the very top of each potato lengthwise. Carefully scoop out the potato flesh, leaving a thin rim to keep the skins intact,  and transfer to a large mixing bowl. Add the butter, and use a potato masher to mash until smooth or to your desired consistency. Next, add the sautéed broccoli, scallions, Italian flat-leaf parsley, cheddar cheese, salt, and black pepper. Stir to combine and adjust the seasoning to taste.

Spoon the prepared filling back into the hollowed potato skins. Return the filled potatoes to the oven and bake for an additional 15 minutes. Serve hot.