Cover potatoes with water and boil until tender when poked with a fork; do not overcook and let the potatoes get mushy. Drain and put them through a potato ricer or food mill (to make sure there are no lumps in the dough).
Immediately add the butter, cream, salt and sugar, and mash together until no lumps remain. Place in a large bowl, smooth the top and cool, uncovered, in the refrigerator overnight.
The next day, preheat the grill to 450 to 500 degrees.
To make lefse: Cut cold mashed potato mixture into quarters. Remove 1 quarter from bowl and put the rest back into the refrigerator.
With your hands, mix in about 3/4 cup flour to the potatoes until well blended. With an ice cream scoop or your hands, measure a golf-ball-size portion of the dough and roll it into a ball. Repeat with remaining quarter. Sprinkle with flour and return to refrigerator.