1. Mix the yeast and the warm water

1. Mix the yeast and the warm water together in a small ramekin. The yeast needs warm water to activate; it will help the doughnut dough rise and stay fluffy. Let activate for 5 minutes.
2. Mix yeast mixture, milk, sugar, salt, eggs, shortening, and 2 cups of the flour in a mixer on a low speed. Alternatively, you can use a wooden spoon and mix by hand, but be sure to mix the dry ingredients first, then the wet ingredients separately, and then combine the two
3. Beat in remaining flour, ½ cup at a time, at a low speed. Do this until the dough no longer sticks to the bowl.
4. Knead the dough with your hands and knuckles for 5 minutes until the dough is smooth but elast
5. Set the dough into a greased bowl to rise. Cover with a towel and let stand until dough doubles in volume (about 1 hour). Dough will be ready when you can press a finger into it and the indentation stays.
6. On a floured surface, roll the dough out until it's about 0.5 inch (1.3 cm) thick.Cut with a floured doughnut cutter, or cut into doughnut shapes by hand.
7. Let the doughnuts rise again until double their size (about 30-60 minutes). Lay them out on a tray and cover them with a large, clean towel.
8. Prepare the glaze while doughnuts are rising. This is a classic butter glaze, not unlike the Krispy Kreme glaze that is popular in America. To make the glaze:
• Melt butter in a saucepan over medium heat. Be careful not to burn the butter.
• Take the butter off the iron and stir in confectioners' sugar and vanilla until smooth.
• Stir in hot water one tablespoon at a time until the icing is thin, but not watery.
9. Heat the oil in a deep fryer or skillet until oil reaches a temperature of 350℉ (175℃). Use a kitchen thermometer for maximum precision.
• To avoid a greasy taste, heat the oil up on medium high for five minutes, and then gently reduce the heat until thermometer reads 350℉ (175℃).
10. Slide the donuts into the oil carefully, with metal tongs or a spatula. Turn the doughnuts over when they float up to the surface. Fry evenly on both sides until golden brown.
11. Remove doughnuts from oil and let drain on a wire rack. Make sure any excess oil drips off the doughnut before you glaze it.
12. While doughnuts are still warm, dip doughnuts into the glaze, coating evenly. Set to dry on a wire rack and enjoy immediately.