Whisk together cake flour, cocoa powder, baking powder, and salt in a medium bowl. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment, mix together sugar and shortening on low speed. Mix until mixture resembles coarse sand. Add yolks and vanilla extract. Mix until creamy. Scrape down bowl as needed to ensure thorough mixing.
Add 1/3 of dry mixture into mixing bowl. Follow with 1/2 of milk. Mix. Add another 1/3 of dry mixture, mix and then add remaining 1/2 of milk. Mix and end with dry mixture.
The dough will be quite sticky. Once combined, transfer dough to a clean bowl. Cover directly with plastic wrap. Refrigerator for one hour (up to overnight).
Fill a large pot with about 3 inches of vegetable oil. Using a candy thermometer, bring oil to 370 degrees F over medium heat.
Remove dough from fridge and transfer to generously floured surface. Dough will be sticky! Sprinkle cake flour as needed to ensure dough doesn't stick to surface. Pat dough into an even layer about 1/2-inch thick.
Dip 2-1/2 inch round cutter in flour each time before cutting dough. Cut smaller doughnut hole in center. Fold and press dough scraps together to cut out more doughnuts.
Brush off any excess flour off the doughnuts before adding them to the hot oil. Depending on the size of your pot, add 3-5 doughnuts to the pot at a time. Be sure not to overcrowd the doughnuts. Set a timer for 1 minutes and 30 seconds. By this time, the doughnuts should have floated to the top. Turn over doughnuts and cook other side for another 90 seconds. Once golden brown all over, remove doughnuts from oil and let drain on paper towels or over a wire rack.
Allow doughnuts to cool before dipping in chocolate glaze.