Sprinkle yeast over warm water and let sit for 5 minutes until foamy.

In a large bowl, mix yeast mixture, milk, sugar, salt, eggs, shortening, and 2 cups of flour. Stir or beat on low until combined.

Add the remaining flour, 1/2 cup at a time, until the dough no longer sticks to the bowl.

Knead the dough for about 5 minutes until smooth and elastic. Place in a greased bowl, cover, and let rise in a warm spot until doubled in size (about 1 hour).

Turn dough onto a floured surface and roll out to 1/2 inch thickness. Cut using a donut cutter.

Place donuts on a floured baking sheet, cover loosely, and let rise again for 30 minutes or until puffy.

For the glaze, melt butter in a saucepan over medium heat. Stir in confectioners' sugar and vanilla. Remove from heat and stir in hot water one tablespoon at a time until smooth and thin (but not watery).

Heat oil in a deep fryer or heavy pot to 350°F. Carefully add donuts, a few at a time. Fry for about 1 minute per side until golden brown.

Remove donuts from oil with a slotted spoon and place on a wire rack to drain.

While still warm, dip the tops of the donuts into the glaze and return to the rack to allow excess glaze to drip off.