Wash and peel potatoes and boil until done. Meanwhile, in a small sauce pan, slowly melt butter over low heat. After it melts, carefully skim the foam from the top of the melted butter. Keep the butter warm over very low heat. This is clarified butter. Whatever butter you don't use, carefully remove the melted butter to a small resealable container. Avoid the milk solids at the bottom of the sauce pan. Discard milk solids.
Halve the onion then slice. Add clarified butter to sautee pan and slowly sweat the minced garlic until just golden. Separate the onions and sautee in clarified butter over medium heat until transluscent. While the onions are cooking, slice the potatoes into disks, about 1/4 inch thick. Add to the onions.
Mince the parsley and add to the potatoes and onions. Sautee the potatoes until they begin to crisp around the edges. There may be some coloring of the potatoes and this is good. Garnish with parsley sprig. Serves 4.