Add the whole milk, water, 2 tablespoons of the sugar and the yeast to the bowl of an electric. mixer fitted with a whisk. Mix on low until just incorporated, then turn off the mixer and let sit for 5 minutes or until frothy.
1 cup whole milk, 3/4 cup water, 2 tablespoons granulated sugar, 2 teaspoons active dry yeast
Add the egg and egg yolks and mix to combine, then mix in the remaining sugar and vanilla extract.
1 egg, 2 egg yolks, 1 teaspoon vanilla extract, 1/2 cup granulated sugar
Turn off the mixer and switch the whisk to the dough hook attachment. Add the flour, then the salt on top of it.
4 cups all purpose flour, 1 1/2 teaspoons salt
Knead the dough until it starts to come together. Add the butter and continue kneading for an additional 5 minutes, until a smooth dough forms.
5 tablespoons salted butter
Remove the dough from the mixing bowl and roll into a ball. Place it back in the bowl and cover with plastic wrap. Let rise in a warm area for 1 hour or until doubled in size.
Once the dough has risen, turn it out onto a lightly floured surface. Roll the dough out to approximately 1/2-inch thickness.
Use a 3-4 inch donut cutter and cut out 12 donuts. You may need to fold and re-roll the dough to get as many donuts as possible.
Place the donuts onto a parchment paper-lined baking sheet. Cover with plastic wrap and allow to rise in a warm area for another hour or until doubled in size.
When it is near the end of the rise time, preheat 3-inches of vegetable oil in a large stockpot to 350°F.
vegetable oil
Once heated, carefully place 4-5 donuts into the oil. Fry for 2-2 1/2 minutes, then flip and continue to fry for an additional 2-2 1/2 minutes or until golden brown.
Remove the donuts from the oil with a slotted spoon allowing the excess oil to drip back into the pot. Transfer to a cooling rack with paper towels under it.
Repeat with the remaining donuts.