Pierce the potatoes several times with a fork or sharp knife, and then cook them in the microwave until they are tender all the way through, about 6-7 minutes, depending on potato size and power of microwave. Flip the potatoes once or twice, and check with the tip of a sharp knife towards the end. (Tip: Poke the knife in the spot where you will later cut the potato in half.) Alternatively, you may bake the potatoes in the oven until tender. Potatoes may be cooked an hour or two in advance and left at room temperature until ready to proceed.
Set the oven to broil. Cut the potatoes in half horizontally, and then score each half in a checkerboard fashion. Cut to the skin but not through the skin. (Don’t worry if they fall apart in a few places. Just push them back together as you place them on the baking sheet.)
Brush the cubes with the melted butter or oil, getting some in the crevices, and then sprinkle all over with the Parmesan and seasoned salt. (I place the potatoes side-by-side on a foil-covered baking sheet. Keeping them close together and in an even layer ensures that most of the toppings land on the potatoes rather than the baking sheet and also allows for more even broiling.) Place the potatoes on the middle oven rack and broil for 10-15 minutes, or until golden brown on top. Watch carefully towards the end until you know how long this takes in your oven.