Place yeast in the 1/4 cup of warm water, add the 1 tsp sugar, stir and let it stand for about 5 minutes until foamy.
Heat milk and shortening in a small saucepan. Let stand until it's lukewarm.
Mix sugar, salt and the egg in a large bowl. Stir in the cooled milk mixture and the pinch of salt. Stir until sugar is dissolved.
Add the yeast mixture and 1 cup of the flour. Mix until a soft batter forms.
Add enough remaining flour until you get a soft dough consistency. The amount of flour is variable in different weather conditions. You may need more flour than stated. The dough should be pretty soft and slightly sticky--it's texture you're aiming for.
Turn the dough out onto a floured surface and knead until smooth--the dough will be sticky.
Place the dough in a lightly oiled bowl, cover and let rise until double--about 1 1/2 hours.
Roll out dough to 1/2-inch thickness. Using a donut or biscuit cutter (I used a large biscuit cutter and a soda bottle cap for the middle hole) cut out the donuts and place them on a floured piece of parchment. Let rise until light--about 40 minutes.
Meanwhile, heat 1-2 inches of oil in a large deep skillet until it's 325-350F/160-180F. Fry donuts until golden brown on each side. I flip them with wooden chopsticks. Don't crowd the pan--fry in shifts. Drain on paper towels.
Mix glaze ingredients and drizzle over warm donuts.
Makes about a dozen medium donuts.