Butter a rimmed 15½x10 ½-inch baking pan (we use a jellyroll pan) and set aside. (A 9x13-inch pan will also do, but the needhams will be thicker.) In a large bowl or the bowl of a standing mixer, add the sugar, potato, melted butter, coconut, vanilla, and salt. Mix on low speed (mixture will be very dry at first) until a thick paste forms; then increase the speed for 30 seconds, or until all of the sugar is completely incorporated.
Transfer the mixture to the prepared pan, and press down evenly. Let the mixture set and firm up at room temperature, about 1 hour. Then cut into small, even squares.
Melt the chocolate and the chips in a double boiler until smooth; then remove from the heat and add the shortening, stirring vigorously until shiny. Now place one coconut/potato square onto the tines of a fork and lower into the chocolate until coated; lift it and let the excess chocolate drip back into the pot. Transfer the square to a sheet of parchment to harden, about 1 hour. Repeat with the remaining squares. Store in an airtight container for up to two days for best flavor and appearance.