Into the bowl of a stand mixer fitted with a paddle attachment, add All-Purpose Flour (2 cup), Instant Dry Yeast (1 package), Sea Salt (1/2 teaspoon), Granulated Sugar (3 tablespoon), Vanilla Extract (1 1/2 teaspoon), yolks of Egg (3), and Whole Milk (1 cup), heated to 110 degrees F or 43 degrees C. Mix until smooth.
Add Vegetable Oil (4 tablespoon) and remaining All-Purpose Flour (1 cup). Mix until dough comes together.
Transfer dough to a bowl. Cover with plastic wrap and let it rise in the fridge for at least 1 hour, or up to 12 hours.
Press the air out of the dough.
Turn dough out onto a lightly floured surface and knead a few times to reduce the stickiness.
Using a donut cutter, cut out circles in the dough.
Cut out smaller circles in half of the donuts. Place finished donuts on a floured baking tray.
Cover with plastic wrap and let rise for 15-20 minutes.
In a pot, heat Oil (to taste) to 300 degrees F (150 degrees C).
Add the donuts into the oil, cooking for about 45 seconds on each side or until golden brown. Remove finished donuts with a slotted spoon.
Into a mixing bowl, add Powdered Confectioners Sugar (1 1/2 cup), Milk (2 1/2 teaspoon), Vanilla Extract (1 teaspoon), and Butter (1 teaspoon). Whisk together until smooth.
Coat the donuts with holes in the glaze. Place finished donuts on a wire rack to let extra glaze drip off.
Cut a small hole in the side of the donuts without holes.
Pipe Jam (to taste) into the donuts.
Dust Powdered Confectioners Sugar (to taste) over the jam donuts.