In a large bowl sprinkle yeast over warm milk with sugar and let stand for 5 minutes, or until foamy. Stir in salt, eggs, shortening, butter, and 2 cups of flour. Mix at low speed in mixer or stir with wooden spoon.
3 cups all-purpose flour
Beat in remaining flour 1/2 cup at a time, until the dough no longer sticks to the bowl. Knead flour about five minutes or until smooth and elastic. Place dough in a greased bowl and cover with a cloth. Set in a warm place to rise until doubled or set in fridge overnight.
Turn dough out onto floured surface and gently roll out to 1/2 inch thickness. Cut with a floured doughnut cutter or a biscuit cutter if making filled doughnuts. Cover loosely and let dough rise again until double in size.
1 Quart vegetable oil for frying
Heat oil in a deep fryer to 350°. Carefully slide donuts into oil. Turn donuts over as they rise to the surface. Fry until golden brown on both sides.
2 cups Confectioners Sugar 4 tablespons Water (room temperature)
Mix together the confectioners sugar and water until smooth. Coat the donuts while still hot and allow to cool on a drying rack.