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 this doughnut cutter and save yourself a lot of trouble!
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). 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.
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, and remove them and place on a paper towel lined platter 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. Using an ISI whipper, pipe fresh cream into a doughnut cut in half (add some jam first if you like).

Notes
-This recipe requires the use of a scale. Please do not attempt to make these without one, as you’ll most likely be disappointed.

-Special equipment: a kitchen scale, parchment paper, cut into about 4″ squares (smaller pieces for doughnut holes) and a pot, deep fryer, or wok and candy thermometer (optional).

-Times for prep, rising and cooking the doughnuts are estimates. It depends on many factors, but the times given are estimated at minimum.