Eggless Doughnuts

Doughnuts are something that would not be rejected when offered to someone. Some major doughnut companies initially did not list eggs as an ingredient in it. But slowly it changed when the law required every allergen to be listed. It was devastating to know that we had been consuming it all these days. Then started my R&D to make at home. Honestly, this recipe is not mine it was taken from different books and altered with my ideas. Of course, neither was I born or brought up in the west to acquire this from my mom or granny. But have to tell you after all those trials this one was satisfying. Well!! Got feedback from friends and family before bragging about it.
Yeast - 2 packs
Water - 1/4 cup warm
milk- 3/4 cups
Sugar - 1/2 cup
Salt - 1/2 tsp
Yogurt - 2 tbsp
Shortening- 5 tbsp
Self rising flour- 5 cups
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, yogurt, shortening, and 2 cups of the flour. Mix for a few minutes at low speed. 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.
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 confectioners' 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. Add little more powdered sugar if it's watery.
5. Heat oil in a deep-fryer. 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.