Leave the skin the potatoes and clean them off under running water. Cut them up into about 3/4 inch chunks. Put them on the stove in pot with enough water to cover them by about an inch to an inch and a half. Add the salt and when they are soft to a poke with a fork drain off the water.
Add the butter and the parmesan cheese. Crush and mix it all together with a whisk or a potato masher or just a fork.
Put skillet on at medium high and add just enough olive oil to coat the bottom. Divide the Parmesan Smashed Potatoes into serving sized portions and add them to the skillet. Flatten them out a little. Give them about 2-3 minutes each side.