With a mandoline or sharp knife, slice the potatoes about 1/16-inch thick. You should have about 6 cups. Place the potato slices in a large bowl and rinse with cold water until the water runs clean. Thoroughly dry the potatoes, first in a salad spinner, then on paper towels. This is important because any moisture left on the potatoes will cause the oil to splatter. Pour the oil into a 6-quart heavy bottomed, straight-sided saucepan, 8 to 10 inches in diameter. The oil should be 1 1/4 to 1 1/2- inches deep and the pan no more than a quarter full. This prevents any bubbling over when frying the potatoes. Heat the oil to 315 degrees on a deep-fat thermometer. (To check the temperature without a thermometer, drop a small piece of bread the size of a crouton into the oil. It should float to the surface and lightly brown in about 2 minutes) Carefully fry the potato slices in 2 or 3 batches until light brown and crisp. You will need to stir the potatoes with a slotted spoon almost constantly to ensure even cooking. Each batch should take 15 to 20 minutes to cook. (If the potatoes brown in much less time, the oil is too hot. This will result in a chip that is neither cooked through nor crisp.) As you remove each batch of crisp potato chips, place them on a cookie sheet lined with paper towels. When all the potatoes are done, place them in a mixing bowl large enough to hold them comfortably. Over a medium flame, heat the butter and garlic over the potatoes, add the chopped parsley, salt and pepper, and mix thoroughly with a rubber spatula. Be careful not to crush the chips. Serve hot. The chips can be made several hours in advance. Store in a tightly closed container and reheat in a 350 degree oven until hot. Toss with the seasoned garlic butter at the last minute.