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

2. In a large bowl, mix together the yeast mixture, milk, sugar, salt, eggs, vanilla, shortening, and 2 cups of the flour. Mix for a few minutes at low speed, or stirring with a wooden 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.

NOTE: While you are preparing the dough. Turn your oven to 200 degrees for 1 minute, then turn off the oven. Then open the door.

Place the dough into a greased bowl, and cover. Making sure that the oven is off. Set in oven to rise until double. Dough is ready if you touch it, and the indention remains.

3. 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 double. Cover loosely with a cloth.

4. Heat oil in a deep-fryer or large heavy skillet to 350 degrees F (175 degrees C). Slide doughnuts into the hot oil using a wide spatula. Turn doughnuts over as they rise to the surface. Fry doughnuts on each side until golden brown. Remove from hot oil, to drain on a wire rack. Dip doughnuts into the glaze while still hot, and set onto wire racks to drain off excess. Keep a cookie sheet or tray under racks for easier clean up.