Place ¼ cup lukewarm water in the bowl of an electric mixer, and sprinkle the yeast over the water. Stir, and then set it aside to activate for 5 minutes.
In another bowl, mix together the bread flour, pastry flour, baking powder, sugar, salt, nutmeg, and powdered milk. Add 1½ cups of this mixture, ¾ cup cold water, the butter, and the egg to the yeast mixture. Combine in the electric mixer fitted with the dough hook on very low speed for 1 minute. Then, over a 1-minute period, add the remaining flour mixture. Increase the speed to medium and mix for 2 minutes. Stop the mixer, scrape down the sides of the bowl with a rubber spatula, and beat on high speed for 2 minutes. Transfer the dough to a large buttered bowl (large enough to let the dough double in size), cover the bowl loosely with a plastic bag (we use plastic garbage bags in various sizes, depending on the size of the pan), and refrigerate it overnight.
The next morning, remove the dough from the refrigerator, turn it onto a floured surface, and roll it down until it’s ½ inch thick. If you’re making jelly-filled doughnuts, cut out 12 rounds with a 3½ inch round cookie or biscuit cutter. If you want to make glazed doughnuts, cut the same 12 rounds and then turn them into rings by cutting a hole in the center of each one with a 1 inch cutter. Line a cookie sheet with a linen napkin and dust it generously with flour. Place the doughnuts and their holes on the prepared cookie sheet. Put the entire sheet in a plastic bag and tie it loosely. Let the doughnuts rise in a warm part of the kitchen until they double in size, about 30 minutes.
While the doughnuts are rising, fill a large heavy-bottomed pot with oil about 2 inches deep, and heat it over medium heat until the oil reaches 350°F on a deep-fry thermometer.
Working in batches, carefully drop the doughnuts, one by one, into the hot oil without overcrowding the pot. Fry until the doughnuts are golden brown, then flip them over and fry the other side-this should take about 4 minutes total. Test for doneness by picking out a sacrificial doughnut and cutting it right in the middle to see if it’s cooked through-this will help you gauge how much more time the doughnuts need. When they’re done, remove the doughnuts with a slotted spoon and place them on a plate lined with paper towels. Continue the process with the rest of the doughnuts and the holes (the holes will fry much faster). Let them sit until they’re cool enough to handle.
To make glazed doughnuts, dip the top of each doughnut into the glaze until half of the doughnut is coated. Shake off the excess. Put the doughnuts, glaze side up, on a cooling rack and let them dry slightly. Then toss the holes in sugar, place them on top of the doughnuts, and serve.
To make jelly doughnuts, use the handle of a wooden spoon to poke a hole three quarters of the way into each doughnut. Gently move it around to create a nice-size cavern for the jam. Put the jam in a pastry bag fitted with a plain decorating tip. Insert the tip into the doughnut and fill it until it feels heavy. Repeat with the rest of the doughnuts. Dip these in the glaze as well.
For the Glaze:
Whisk all the ingredients together in a bowl until a smooth glaze is formed. Keep covered until ready to use.