Combine, 2 cups (250g) flour, yeast, sugar, and salt in the bowl of a stand mixer that’s been fitted with a paddle attachment. Stir well.
Combine milk and butter in a small saucepan. Heat over low heat until butter is melted and mixture reaches 110-115F (43-46C). If mixture becomes too hot, allow it to cool to the indicated temperature before proceeding.
Pour milk/butter mixture over dry ingredients and stir until completely combined.
Combine eggs and vanilla extract and use a fork to lightly scramble. Add to mixing bowl and stir on low-speed until completely combined.
Switch paddle attachment out for a dough hook and, with mixer on low speed, add remaining flour (190g) until the dough forms a soft ball that is pulling away from the sides of the mixing bowl. You may need to add more flour to get the right consistency, add additional flour one tablespoon at a time until proper consistency is reached (see video below recipe for a visual).
Transfer dough to a large lightly oiled bowl and cover. Place in a warm spot until doubled in size, about 30 minutes.
Once dough has doubled in size, transfer to a lightly floured surface and roll out to ½” thick. Use a donut cutter to cut out donuts and transfer to a parchment paper lined baking sheet. Cover with plastic wrap and leave in a warm place to rise for another 30 minutes or until donuts have puffed.
While donuts are rising, fill a medium-sized saucepan about 2” deep with oil. Turn stovetop heat to medium¹ and heat oil to 350-355F (175-180C).
Once donuts are finished rising and oil has reached temperature, fry donuts one at a time until light golden brown, for me this was about 60 seconds on each side. Make sure to allow oil to come back to the indicated temperature before cooking each donut.
Allow donuts to cool for a minute or two after frying, then coat with granulated or powdered sugar if desired. If glazing donuts, allow donuts to cool before glazing.
Instructions for glazed donuts
To make glaze, whisk together sugar, melted butter, vanilla extract, and hot water until smooth. Dip donuts in glaze on both sides, then transfer to a cooling rack and allow glaze to harden before enjoying.
¹Do not crank the heat up to high to speed up the process, if you do it will quickly surpass the recommended temperature and you’ll have to wait for it to cool back down. Maintaining a consistent temperature is critical for good donuts. If you cook donuts on too high of a heat they’ll be burned on the outside and raw on the inside. If you use too low of a heat they will be greasy. Do a test donut first and cook until just beginning to turn golden brown and always allow oil to come back to temperature in between donuts. Donuts are best when served warm the same day they are made, but these will keep for two days if stored in an airtight container at room temperature