In a large bowl, dissolve yeast in lukewarm water.
In a saucepan, heat milk over medium heat until scalded. Remove from heat, add butter, shortening, sugar, salt and mashed potatoes to scalded milk.
When cool, add milk mixture and eggs to the yeast, whisking thoroughly. Stir in enough flour to make a stiff dough. Pour dough into a buttered bowl, cover and place in the refrigerator for several hours or overnight.
When ready to make rolls, punch down the dough and form into rolls. Place rolls in two lightly greased 9 x 13-inch baking dishes. Cover and let rolls rise about 2 ½ hours. Bake at 400 degrees for 10-12 minutes or until golden brown.
Cook's Note: This dough makes wonderful cinnamon rolls too.