To make the glaze: Combine the confectioners' sugar with 2 tablespoons of water in a small bowl. Mix well then add a little more water, if necessary, to make a smooth, creamy glaze. Cover the glaze directly with plastic wrap and reserve. (For tips on making flavored glazes see the Cook's Note below.) To make doughnuts: Heat the milk in a saucepan over medium-heat. When the milk reaches a simmer pour it into a mixing bowl and allow it to cool.
Meanwhile, measure 1/4 cup of lukewarm water into a small bowl. Sprinkle the yeast into the water then let the mixture stand until the yeast dissolves, about 7 minutes. Stir the yeast mixture into the milk along with 1 tablespoon of the sugar. Mix in 1 1/2 cups of the flour (by hand or with an electric mixer) then cover the dough starter with a clean towel and set it aside to rise and rest in a warm place for 1 hour. When the dough has relaxed, cream the butter with the remaining 1/4 cup of sugar. Beat the butter mixture into the dough a little at a time. Mix in the egg and salt then mix in the remaining 3 cups flour. Work the dough until it is smooth then place it in a well-greased bowl. Cover again with a clean towel and set aside in a warm place until doubled in bulk, at least one hour.
Turn the dough out onto floured board and roll it out about 1/2-inch thick. Using a floured doughnut cutter, cut out the doughnuts. Transfer the doughnuts to a clean floured board or baking sheet. Cover once again with a clean towel, and set aside to rise until doubled. Heat about 2 inches of oil in a deep pot over medium-high heat until the oil reaches 375 degrees F. Working in batches of 2 or 3, fry the doughnuts until they float. Once they bob to the surface of the oil, carefully flip them over. Continue cooking, turning as necessary, until the doughnuts are uniformly golden-brown.
Transfer the cooked doughnuts to a plate lined with paper towels to drain. While the doughnuts are still warm, dip 1 side of each into the glaze then set aside to cool until the glaze firms. Serve warm or at room temperature.
You can alter the basic glaze recipe by substituting fruit juice or liqueur for some or all of the water.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.
Recipe courtesy of Mark Isreal, Doughnut Plant, New York, NY