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Wash and dry the potatoes well. Rub them all over with the olive oil. Sprinkle the potatoes with salt.
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Bake these at 400 degrees for 30 minutes. Then flip them and bake them for another 10 minutes, or until they are fork tender.
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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.
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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.
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Stir in ½ cup shredded cheddar and 1 cup broccoli florets.
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Divide the filling mixture evenly among the 8 potato halves.
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Divide the remaining cheddar cheese among the 8 potato halves as well. (Just sprinkle a little onto the filling of each potato.)
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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.)