Ingredients:

Dough:
2 packest active dry yeast
1/4 cup warm water (105 to 115 degrees)
1 1/2 cups lukewarm milk
1/2 cup white sugar
1 teaspoon salt
2 eggs
1/3 cup shortening
5 cups all-purpose flour
1 quart vegetable oil for frying

Glaze:
1/3 cup butter
2 cups powdered sugar
1 1/2 teaspoons vanilla
4 tablespoons hot water or as needed – I often end up using more as the glaze stiffens as it sits.

Directions:

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, 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. 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.
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. Melt butter in a saucepan over medium heat. Stir in powdered sugar and vanilla until smooth. Remove from heat, and stir in hot water one tablespoon at a time until the icing is somewhat thin, but not watery. Set aside.
5. Heat oil in a deep-fryer or large heavy skillet to 350 degrees F. 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. Place a brown paper grocery sack under the rack for easier cleanup.