In the bowl of a stand mixer, whisk together warm milk, yeast, and one teaspoon of sugar. Let mixture sit for 5-7 minutes until bubbly and aromatic.
Whisk in remaining sugar, eggs, egg yolk, and salt until smooth.
Attach dough hook to mixer. With the mixer running on low, add flour in three additions. Between the second and third addition, add shortening one tablespoon at a time.
Increase to medium speed. Knead dough for 3-5 minutes until mixture forms a smooth dough that no longer sticks to the sides of the bowl.
Transfer dough to a large greased bowl. Cover bowl and let sit at room temperature for one hour, or until doubled in volume.
Punch down risen dough. On a floured surface, roll dough to about 1/2-inch thick. Using a 4-inch round cutter, punch out doughnuts. Loosely cover rounds with plastic wrap. Let rest for 30 minutes until doughnuts are puffy.
Add frying oil to a large heavy bottomed sauce pot such as a Dutch oven or cast iron. Set over medium heat until oil reaches 360°F (or 182°C).
Brush off any excess flour from dough. Carefully place 2-3 donut rounds into hot oil. Do not overcrowd. Cook for 90 seconds on each side, until golden brown*. Use a slotted spoon to transfer donuts onto a paper towel lined baking sheet.