In the bowl of your stand mixer with the paddle or the whisk attachment, cream the softened butter and the sugar on medium high speed until the mixture is light in color and fluffy.
While mixing on low, add in one egg, let it mix in and then add in the second egg and mix on medium speed until everything is smooth and combined
Add in the buttermilk and the vanilla and mix until combined
While mixing on low, add in the flour, salt, baking powder, baking soda, and nutmeg and mix until the dough is combined. Do not over-mix. The dough will be sticky.
Lightly flour your work surface and transfer the sticky dough to the floured surface.
Press the dough down lightly until its about 1" thick.
Fold the dough over onto itself 3-4 times until the dough is smooth.
Flatten the dough down to about 1/2" or use a rolling pin. Let the dough rest for 5-10 minutes while your oil is heating up.
Turn on your FryDaddy or begin heating your oil to 360ºF-375ºF (182ºC -190ºC). Set up a draining station for the donuts by placing a cooling rack over a sheet pan to catch the oil.
Use a donut cutter or ring cutter to cut out the donuts. You can press together the scraps and roll them out again to get as many donuts as you can. Just keep in mind the more you work the dough, the tougher the donuts will get.
Add the donut to the hot oil using your slotted spoon to lower it gently. Fry the donut for 2 minutes then flip it over and fry it for 1 more minute.
Fry your donut holes for about 1 minute, stirring and pushing them down with your spoon until golden brown on the outsides.
Transfer the dough to a cooling rack over a sheet pan to let the oil drain away from the donut
Once your donuts are cooked you can roll them in powdered sugar, cinnamon sugar, glaze them with donut glaze or chocolate glaze!
Store donuts in a paper bag at room temperature for up to two days. They are best eaten fresh! Do not refrigerate.