Wash and dry the potatoes well. Rub them all over with the olive oil. Sprinkle the potatoes with salt.
Bake these at 400 degrees for 30 minutes. Then flip them and bake them for another 10 minutes, or until they are fork tender.
Cut each of the potatoes in half the long way. Remove most of the potato from the skins (like a hollowed out boat). Place the potato insides into a medium sized bowl.
To the medium bowl, add the ½ cup sour cream, 2 Tablespoons melted butter, ½ teaspoon salt, ¼ teaspoon pepper, and ¼ teaspoon garlic powder. Use a hand mixer to combine this well.
Stir in ½ cup shredded cheddar and 1 cup broccoli florets.
Divide the filling mixture evenly among the 8 potato halves.
Divide the remaining cheddar cheese among the 8 potato halves as well. (Just sprinkle a little onto the filling of each potato.)
Bake the potatoes at 350 degrees for 7 minutes. (You will have to bake these in batches. Make sure there is room for the air to circulate around them.)