Mix potatoes, shortening, and half-and-half in a bowl; cover with plastic wrap and let stand 8 hours or overnight.
Combine flour, salt, and sugar with the potato mixture. Stir dough until uniform and form into 12 small balls.
Place balls in refrigerator; remove one at a time to keep the rest cool. Roll dough out on a floured surface using a floured rolling pin, into a very thin circle slightly smaller than the diameter of your skillet. Use more flour as needed to prevent sticking.
Heat a lefsa pan or skillet over medium-high heat. Cook the dough circle until bubbles form, about 1 minute; flip and cook until done, about 30 seconds.
Repeat rolling and cooking steps with the remaining dough.
