Preheat oven to 375°F. Cut a thin slice from the bottom of each potato to provide a steady base. 

Place parchment paper or a cloth kitchen towel on a cutting board, then arrange one chopstick (or wooden spoon) lengthwise on parchment paper and place a potato lengthwise alongside the chopstick so the potato is nearest you. Slice potato crosswise into ¹⁄8-inch-thick slices. The chopstick will prevent the knife from cutting all the way through the potato. Repeat with remaining potatoes.

Gently rub potatoes with olive oil and arrange on a baking pan, sliced sides up. Sprinkle with salt. Cover tightly with foil and bake 1 hour. 

In a small bowl, combine butter, parsley and Parmesan cheese. Uncover potatoes and brush with butter mixture. Increase oven temperature to 450°F. Bake for 10 to 15 minutes more or until tender.