In the bowl of a stand mixer fitted with the paddle, stir yeast in the warm milk. Add 2 cups of the flour. Mix and let stand about ½ hour, until very bubbly.

In the meantime, beat the egg yolks and whole egg until light and fluffy (about 5 minutes).

To the proofed yeast, add the melted butter, sugar, salt and vanilla one at a time. Add beaten eggs and mix until well blended. Switch to the dough hook and slowly add the rest of the flour to the bowl and knead on low speed until a very soft dough forms. You may not use all of the flour.

Cover the bowl and let rise in a warm place until doubled (about 2 hours).

When the dough has doubled, uncover and punch down. Pat dough onto a floured work surface, down to ½ inch.

Using a cookie cutter, glass, or doughnut cutter, gently cut circles and place on parchment paper lined baking sheets. Wax paper may also be used. Cover and let rise for 20 minutes.

Heat oil in cast iron skillet, deep fryer, or dutch oven to 350?F. Working with 3 to 4 at a time, drop doughnuts into the oil and fry on one side until golden brown. Turn over and fry the other side until golden brown. Using tongs, remove the fried doughnuts and drain on paper towels. Let cool completely, then sprinkle with powdered sugar or desired icing. You may also cut them in half and fill with your choice of custard or fruit preserves before topping with the powdered sugar.

Source: Adapted from Epicurious forum user cynthy123