Activate yeast mixture:

In the bowl of a stand mixer, stir together the yeast and warm water; allow to sit for 10 minutes until it becomes frothy.

Mix dough ingredients:

Pour in the milk, sugar, salt, eggs, shortening, and 2 cups (250 g) of flour. Beat on medium speed for 2 minutes. Incorporate the remaining 3 cups (375 g) of flour and mix only until unified.

Proof the dough:

Take the bowl off the mixer, cover with a clean kitchen towel, and let it proof in a warm area for 1 hour, until pressing a finger into the dough leaves an indentation.

Cut out doughnuts:

On a lightly floured surface, roll out half the dough to a thickness of 1/2 inch (1.3 cm). Dust a doughnut cutter with flour and stamp out doughnuts. Arrange them on wax paper. Repeat with the other half to produce 24 doughnuts total.

Second rise:

Cover the doughnuts and let them rise in a warm spot for 30–45 minutes (I used 45).

Heat frying oil:

In a cast-iron skillet or deep saucepan, warm the vegetable shortening to 375°F (190°C). Rely on a thermometer to confirm the temperature.

Fry doughnuts:

Fry each doughnut for 90 seconds per side. Transfer to a cooling rack to drain.

Make glaze and dip:

To prepare the glaze, whisk together confectioners' sugar, milk, and corn syrup in a bowl. Microwave the mixture for 30 seconds. Immerse the cooled doughnuts in the glaze.

Serve immediately:

Serve right away, indulging without restraint.