Sprinkle yeast over warm water and let stand for 5 minutes, or until foamy.

In a large bowl, mix together the yeast mixture, milk, sugar, salt, eggs, shortening, and two cups of the flour. Mix for a few minutes at low sped, or stirring with a wodden spoon. Beat in remaining flour 1/2 cup at a time, until the dough no longer sticks to the bowl. Knead for about 5 minutes, or until smooth and elastic. Place the dough into a greased bowl and cover. Set in a warm place to rise until double. Dough is ready if you touch it and the indention remains.

Turn the dough out onto a floured surface, and gently roll out to 1/2 inch thickness. Cut with a floured doughnut cutter. Let doughnuts sit out to rise again until doubled. Cover loosely with a cloth. Can sprinkle a little flour on top and loosely cover with plastic wrap and place in fridge overnight. Take out of fridge and let rest till warm on counter, about one hour.

Melt butter in saucepan over medium heat. Stir in confectioners sugar and vanilla till smooth. Remove from heat, stir in hot water one tabelspoon at a time until the icing is somewhat thin, but not watery. Set aside.

Heat oil in a deep-fryer or large heavy skillet to 350°F. Slide doughnuts into the hot oil using a wide spatula. Turn doughnuts over as they rise to the surface. nFry doughnuts on each side until golden brown.b Remove from hot oil, to drain on wire rack. Dip doughnuts in glaze while still hot, and set onto wire racks to drain off excess. Keep a cookie sheet tray under racks for easier clean up.