Preheat oven to 400 degrees F. Place whole potatoes directly on oven rack or on a baking sheet. Bake for about 1 hour, until very tender when pierced with a fork. Let cool until safe to handle.
Slice each potato in half lengthwise. Carefully scoop out most of the flesh into a large mixing bowl, leaving about a quarter-inch of potato attached to the skin. Rub the outside of the skins lightly with olive oil and place on a parchment-lined baking sheet.
Add the butter to the potato flesh and mash until fairly smooth. Stir in the Greek yogurt, buttermilk, salt, pepper, chives, garlic powder, onion powder, dried onion flakes, dill weed, paprika, about 1 cup of the broccoli, and 1 and 1/4 cups of the cheddar cheese. Mix until well combined and creamy.
Divide the filling evenly among the potato shells, mounding it slightly. Top with the remaining broccoli and cheddar cheese. Bake for 20 to 25 minutes, until the cheese is melted and bubbly and the potatoes are heated through. Serve immediately.