Preheat the oven to 400°F (200°C).
Scrub the potatoes clean and pat them dry.
Rub each potato with olive oil and sprinkle lightly with salt.
Place the potatoes on a baking sheet and bake for 50–60 minutes until tender when pierced with a fork.
While the potatoes bake, steam or boil the broccoli florets for 4–5 minutes until tender. Drain and chop into smaller pieces.
Once the potatoes are cooked, slice each potato lengthwise.
Scoop some of the potato flesh into a mixing bowl, leaving a thin layer inside the skins.
Add the scooped potato, butter, sour cream, milk, garlic powder, salt, and black pepper to the bowl and mash until smooth.
Stir in the steamed broccoli and 1 cup of the shredded cheddar cheese.
Spoon the mixture back into the potato shells.
Sprinkle the remaining ½ cup cheddar cheese on top.
Return the stuffed potatoes to the oven and bake for 10–15 minutes until the cheese melts and the filling is hot.
Remove from the oven and top with green onions or extra sour cream before serving.