Combine water and yeast in a stand mixer and let rest for 10 minutes.
Add the milk, sugar, salt, eggs, shortening and 2 cups of the flour.
Turn the mixer on medium speed for 2 minutes, then add the rest of the flour and mix until combined.
Cover bowl and let it rise for an hour or until you can push down on the dough and your fingerprint stays.
Working with half the dough at a time, roll out to 1/2 inch thick on a floured surface.
Dip your cookie cutter or doughnut cutter in flour and cut out as many as you can, probably about a dozen for each half of the dough and place them onto wax paper or a floured surface.
Let rise in a warm spot for 30-45 mins.
In a cast iron pan or other saucepan, heat the vegetable shortening or oil to 375 degrees.
Fry the doughnuts on each side for 90 seconds.
To make the glaze, add the powdered sugar, milk and corn syrup to a bowl and microwave for 30 seconds.
Drain on a cooling rack until you finish cooking them, then dip into the glaze.