1/4 cup water (105-115 degrees)
1 1/2 cups lukewarm milk (scalded, then cooled)
1/2 cup sugar
1 teaspoon salt
1/3 cup shortening
5 cups all-purpose flour
1/3 cup butter
2 cups powdered sugar
1 1/2 teaspoons vanilla
4-6 tablespoons hot water
Dissolve yeast in warm water in 2 1/2-quart bowl. Add milk, sugar, salt, eggs, shortening and 2 cups flour. Beat on low for 30 seconds, scraping bowl constantly. Beat on medium speed for 2 minutes, scraping bowl occasionally. Stir in remaining flour until smooth. Cover and let rise until double, 45-90 minutes. (Dough is ready when indentation remains when touched.) Turn dough onto floured surface; roll around lightly to coat with flour. Gently roll dough 1/2-inch thick with floured rolling pin. Cut with floured doughnut cutter (Or a wide mouth canning ring and a baby block for the center…) Cover and let rise until double, 20-30 minutes. Heat vegetable oil in deep fryer to 375°. Slide doughnuts into hot oil with wide spatula. Turn doughnuts as they rise to the surface. Fry until golden brown, about 1 minute on each side. Remove carefully from oil (do not prick surface); drain. Dip the doughnuts into creamy glaze, then set on rack.
Creamy Glaze: Heat butter until melted. Remove from heat. Stir in powdered sugar and vanilla until smooth. Stir in water, 1 tablespoon at a time, until desired consistency.