Add the milk to a heat-safe measuring cup, and heat to roughly 95°F (too hot and you'll kill the yeast!). I recommend giving it short blasts in the microwave and checking the temp every time. Once heated, whisk in the instant yeast, making sure the yeast is well mixed. Next, whisk in the granulated sugar. Let rest at room temp while prepping the rest of the ingredients, the yeast will start coming alive in the meantime. This means light and airy donuts!
In a small bowl, combine the 2 whole eggs and 1 egg yolk and whisk lightly to combine. In the bowl of a stand mixer with the dough hook attachment, add the milk/yeast mix, followed by the whisked eggs. Begin mixing the wet ingredients on medium speed, letting them start to come together while getting the flour ready.
In a large bowl, measure out your flour (I say this often, but I HIGHLY recommend baking by weight if you can, you results will be so much more consistent). Add the fine sea salt and whisk well to combine.
With the stand mixer on medium, begin adding the dry ingredients one large spoonful (3-4 tbsp) at a time. Pause if necessary to scrape down the sides of the bowl. Once all your flour has been added, let the mixer go a minute or two until a dough has begun to form (if you're already there, then skip this) and then reduce to medium-low and knead for 2-3 minutes.
With the mixer still going, begin adding your softened butter 1-2 tbsp at a time. Room temp is very important here, or the butter will never incorporate correctly. Once all the butter has been added, let the mixer keep going for 5-10 minutes, or until a nice smooth dough has formed (this can take a bit, the greasy butter can cause the dough to slip around in the bowl and take a bit to incorporate, that's ok). You know you're done when the dough looks uniform and is starting to pull from the sides of the bowl. IT WILL BE STICKY! That's expected, don't worry.
Gently scoop the dough out into a large, well greased bowl, then cover with plastic wrap and let rise at room temp for ~1.5 hours, or until doubled in size.
Once risen, dust with flour and gently degas the dough, and then transfer to a well floured work surface. Dust with more flour and then roll out to a large rectangle that's 3/4" thick.
Using either a donut cutter or two biscuit cutters, I recommend 3" & 1", cut out your donuts and gently transfer them to a floured baking sheet (you will likely need 2). Keep the donut holes too! They fry up easily and are your bonus snack for your hard work. If desired, you can gather up the excess dough from cutting, knead it together for a minute or two, then let it rest for about 5 minutes before rerolling to cut more donuts.
Cover the doughnuts with plastic wrap and again allow to rise at room temp for about 45 mintues; they should look nice and puffy when ready.
