Peel the potatoes, then slice potatoes and onion thinly. Ditalini uses a mandoline hand slicer, as shown.
Heat a small amount of butter and olive oil in a pan (enough to coat the bottom of the pan). Layer the onions and potatoes. Sprinkle with salt and pepper. Flip with a spatula halfway through cooking. Be careful not to get the oil too hot or to overcook the onions.