Scald milk. Stir in sugar, salt, and butter. Cool until lukewarm. Measure water into a large bowl. Sprinkle in yeast and dissolve it. Add milk mixture, egg and ½ of the flour. Beat until smooth. Stir in more flour to make a soft smooth dough. For lightness only add enough flour to make a dough you can handle. Turn onto a lightly floured board or pastry cloth. Knead until smooth and elastic (5-10 minutes). Place dough in a greased bowl, turn bottom side up so topside is greased. Cover with a damp cloth; let rise in a warm place until doubled (1 hour). Punch down. On a lightly floured surface roll about ½ inch thick to make a rectangle. Cut doughnuts. Place doughnuts on oiled baking sheets, about 2 inches apart. Cover with inverted baking pans or cloth and let rise until doubled in size (about 1 hour).
About 15 minutes before the end or the rising period, heat fat in deep fryer or electric skillet to 375º.
Handle the doughnuts as gently as possible so the will not fall. Fry a few at a time in deep fat 2-3 minutes or until brown on both sides. Turn doughnuts only once.
Drain on absorbent paper.
Dip in glaze or granulated sugar while still warm and drain them on a rack over waxed paper
Blend 2 c. confectioners sugar, ⅓ c. milk and 1 tsp. vanilla.
*you can reuse the glaze that drips off the already glazed doughnuts