FOR THE DOUGHNUTS:

Heat the milk to 105 degrees. Stir in the yeast until it is dissolved. Transfer to a bowl and add the 5 1/2 ounces of flour. Stir until it forms a smooth paste. Cover the bowl in plastic and place in a warm spot to rise.

When the paste has doubled in size (about an hour, depending on the temperature, it will now look more like a sponge), add it to a stand mixer fitted with a paddle attachment. Rub the seeds from the vanilla bean into the sugar and add to the dough with the mixer on low speed. Add the egg yolks and salt and mix until smooth. Add the butter and mix well. Slowly add the rest of the flour. Keep mixing until it just comes together as a dough. It will be wet and sticky but should be able to hold together.

Brush a large bowl lightly with vegetable oil. Place the dough in the bowl and cover with plastic wrap. Place in a warm spot to rise. Once the dough has doubled in size (about 1-2 hrs), put in the fridge for 15 minutes. This will make it easier to roll out.

On a well floured surface, gently roll out the dough to about 1/2" thickness. Use a doughnut cutter to stamp out the doughnut shapes. Place the stamped dough on a floured and parchment lined sheet pan, cover loosely with plastic and allow to rise again in a warm spot. While you are waiting, work on the glaze.

DOUGHNUT GLAZE:

Split and scrape the seeds from the vanilla bean and rub into the granulated sugar. Whisk the vanilla sugar with the rest of the ingredients in a small bowl until smooth. If the glaze is lumpy, pour it through a fine mesh strainer.

Once the doughnuts have almost doubled in size, about 20-30 minutes, begin heating 2 inches of peanut oil in a large pot. When the oil reaches 350 degrees start frying the doughnuts in batches. Fry them until golden brown on each side. The total frying time will be under 2 minutes.

Allow to drain on a wire rack over a sheet tray. While still warm, drizzle with the glaze.