FOR BREAD MACHINE:

Cup of Yum
1. Place the water, buttermilk, beaten egg, and melted butter in the bread machine pan, then add the dry ingredients which were weighed on a scale (it's so important), except for the yeast.
2. Make a small indentation in the dry ingredients, then add the yeast. Set the bread machine on the ‘dough’ setting.

FOR STAND MIXER WITH DOUGH HOOK, OR BY HAND:

1. Place the dry ingredients in a bowl. Put the lukewarm water in a cup and sprinkle the yeast on top, set aside for about 5 minutes, until the yeast begins to react (you can add a pinch of sugar to help it).
2. Make a well in the center of the dry ingredients, then pour in the buttermilk, egg, melted butter, and yeast mixture. If using a stand mixer, run with the dough hook until a dough forms then continue for about 5 minutes.
3. By hand, knead for about 10 minutes. Cover and set aside until at least doubled in size (usually 1 to 2 hours, depending on the freshness of the yeast, temperature of the water and ambient temperature).

BOTH BREAD MACHINE, STAND MIXER/HAND INSTRUCTIONS FOLLOW BELOW:

1. Once the dough has doubled, place it on a floured surface and knead lightly. Divide it in half, keeping half the dough covered, so it doesn’t form a skin. With a rolling pin, roll out half of the dough to about 1/2″ thickness. Cut with a round, sharp cookie cutter (about 3″ diameter) then make the holes with a smaller cookie cutter (about 1″ diameter), saving the holes. Or splurge (haha) and buy a doughnut cutter and save yourself a lot of trouble!
2. Place each doughnut on a piece of parchment or waxed paper, then place on a cookie sheet. Put the tray in the oven (turn it on for 1 minute, SET A TIMER, then turn it off again, just to make it barely warm).
3. Next, boil some water and pour it into a measuring jug. Place the jug of water in the oven with the tray of doughnuts (this will create steam will keep a skin from forming). With the remaining dough, divide into quarters, then divide each piece in half to make 8 equal amounts. Roll each piece of dough into a smooth ball, and place on parchment or waxed paper pieces and place on a cookie sheet; place in the oven with the other doughnuts to rise until doubled in size.
4. Heat the oil to about 350ºF (180℃). If you don’t have a thermometer, test the oil with a doughnut hole: if it doesn’t start frying immediately, the oil is too cold, if the hole turns brown right away, the oil is too hot. Adjust the heat accordingly.
5. Drop the doughnuts into the hot oil using the paper to carefully lower them into the oil. Turn them over as soon as they become golden brown on the underside, and remove them and place on a paper towel lined platter once they are ready.
6. When the doughnuts have cooled, dip them in the glaze and place on a rack to set.

Glaze Recipe

1. Pour milk or water into sugar in a bowl and stir until it has a smooth consistency (add more or less of each ingredient as desired).
2. Glaze the doughnuts.