1 cup scalded milk
1/2 cup butter
1/2 cup sugar
1/2 teaspoon salt
2 eggs plus 1 egg yolk, beaten
2 envelopes active dry yeast
4 cups sifted flour
Cooking Oil - In the US, blue label Crisco is best. In the UK use Pura or Trex. If you use liquid vegetable oil, the doughnuts will absorb too much oil and be greasy (ick!).
In a large mixing bowl, pour scalded milk over the butter, sugar and salt. Stir until the butter is melted. Cool slightly and add the beaten eggs. Then add the yeast. Let mixture stand for 5 minutes. Blend in the flour a little at a time. Mix into a soft dough. Turn the dough out onto a floured work surface and knead gently for about 2 minutes. Place the dough in a greased bowl, turning to coat all sides. Let rise for 1 hour. Punch the dough down and divide in half. On a lightly floured board roll each section to 1/2-inch thickness. Cut with a floured doughnut cutter. Place on waxed paper. Set in a warm place. Let rise for 30 minutes.
In a deep skillet or fryer heat cooking oil to 375F . Gently slip each doughnut into the oil. Fry for 2 minutes or until golden brown, turning once. Drain on paper towels.
In another mixing bowl, blend 3 cups sifted confectioners or icing sugar, 1/8 cup warm water and 1/2 teaspoon vanilla extract. Stir the glaze until all lumps are gone. If the glaze is too thick, carefully add more water - drop by drop. If it is too thin, add more icing sugar.
I find that if you place a cooling rack over an empty bowl then dip the doughnuts in the glaze and let them drain on the cooling rack, letting the empty bowl catch the drips, you get much better glaze coverage.
My youngest boy suggests rolling the doughnuts in granulated sugar instead of glazing them is much easier. It is. You can also try adding a bit of cinnamon to the granulated sugar before rolling the doughnuts in it. Yum!