- In a bowl, combine buttermilk, oil and egg yolks.
- In a large bowl, with a wooden spoon or a stand mixer using the dough hook, combine flour, sugar, yeast and salt. Add liquids and stir until dough forms into a ball, about 3 minutes. On a floured work surface, knead for 2 minutes or until smooth. Place in a lightly oiled bowl. Cover with a damp cloth and let rise for 1 hour in a warm and humid place (see note).
- On a floured work surface, cut dough in half. Roll out dough, one piece at a time, onto an 8 to 10-mm (1/2-inch) thick sheet. Cut doughnuts with a 7.5-cm (3-inch) round cookie cutter, and then cut out holes with a 2-cm (3/4-inch) small round cutter. Reuse scraps. Place on a floured baking sheet. Cover with a dry cloth and let rise for 30 to 45 minutes in a warm and humid place or until doubled in size.
- Heat shortening or oil in the deep fryer to 185 °C (365 °F). Line a baking sheet with paper towels and place a wire rack on second baking sheet.
- Place icing sugar in a bowl.
- In a small saucepan, heat milk and butter until melted. Add to icing sugar and whisk until sugar has dissolved. Set aside while frying doughnuts.
- Place 3 or 4 doughnuts at a time into hot oil and fry for 2 to 3 minutes or until golden brown, turning halfway through cooking. Beware of splattering. Drain on paper towel and let cool for 1 minute. Dip the doughnuts, one by one, into glaze. Drain on wire rack and let cool for about 15 minutes.
Sugar-glazed doughnuts are best eaten the same day.
Dough scraps can be reused, but reworked dough does not make for as smooth and perfect doughnuts.
Heat the oven for about 2 minutes or until just warm. Turn it off, but leave oven light turned on. Place a cup of very hot water with the bowl or baking sheet containing dough. Leave to rise as indicated in recipe.