Preparation

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  Place the water, buttermilk, beaten egg and melted butter in the bread machine pan or stand mixer bowl, then add the dry ingredients, except for the yeast.
  Make a small indentation in the dry ingredients, then add the yeast.
  Set the bread machine on the ‘dough’ setting.
  If using a stand mixer (see directions in printable recipe below, as steps with the yeast are different), run it with the dough hook, until a soft dough is formed, then cover and set aside until at least doubled in size.
  Once the dough has risen, 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 doughnut cutter (about 3″ diameter). Or use a sharp cookie cutter, then make the holes with a smaller cookie cutter (about 1″ diameter), saving the holes.
  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).
  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).
  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.
  Heat the oil to about 350ºF (180º). 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.
  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, then remove and place on a paper towel lined plate once they are ready.
  When the doughnuts have cooled, roll them in sugar to coat evenly.
  If you choose to fill the large doughnuts, push a skewer into the center of the doughnut to make a hole, then place some room temperature jam, or slightly warmed Nutella into a piping bag and pipe the filling into the doughnut.