Dissolve yeast in water.
Combine milk, sugar, salt, egg, shortening and add to yeast water.
Slowly beat in flour on low until smooth elastic.
Roll dough into a ball, place in a bowl and cover.
Let rise until doubled, about 1 hour.
Roll out on floured surface about 1/2 inch thick.
Cut with a donut cutter or any circular glass and use a smaller circle to cut out the center (doughnut holes). Separate the doughnut centers (holes) from the doughnut rings.
Place on a cookie sheet and allow enough room to let them rise. Let rise for about 30 min. Heat vegetable oil to 375 degrees.
While donuts rise, combine cinnamon and sugar in one bowl and powdered sugar in another bowl. If icing donuts, prepare icing. These need to be ready before frying so the hot doughnuts can be coated immediately.
Slowly transfer doughnuts with spatula to the hot oil and fry 30 seconds each side until lightly golden brown.
Place them in the immediately in your coating of choice and shake bowl side to side to coat evenly. Add sprinkles to iced donuts.
Cool donuts on a wire rack until ready to serve.