Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper.
Scrub and dry the potatoes, then rub the skins with olive oil. Place potatoes on the baking sheet and bake for 1 hour, or until soft. Remove from the oven and set aside to cool.
Once the potatoes are cool to the touch, slice them in half lengthwise. Carefully scoop out the potato innards and place them into a large bowl, leaving a thin rim around the insides of the skins. Return the skins to the baking sheet.
To the potato innards, add butter, cream, sour cream, and seasonings. Use a potato masher or hand mixer to blend until smooth. Using a rubber spatula, fold in the broccoli and half of the cheese.
Divide the filling evenly among the potato shells, then top with the remaining cheese. Bake 20-25 minutes, or until the cheese is melted and the potatoes are heated through. Broil for 1-2 minutes if desired.
The potatoes will be very hot when you take them out of the oven, let them cool on the worktop for 10 to 15 minutes before cutting them in half.
Leave a thin piece of flesh around the potato skin so that they hold their shape.
You can finish off the broccoli cheese twice baked potatoes under the broiler to get the cheese nice and bubbly.