Mix together ingredients for glaze. Melt butter in hot milk, add 1 tsp sugar and salt. Allow to cool. Beat in yeast, nutmeg, eggs, remaining sugar, and 3 cups flour. Add rest of flour (dough will be sticky).

Knead for 5 minutes then allow to rise for 1-1 1/2 hours. Roll out dough, cut into shapes. Do not re-roll dough, then allow to rise for 30-45 minutes. Heat oil to 365° and fry 1 - 2 minutes on each side or until brown. Toss in the doughnut holes first, let those cook, and then proceed to cooking the donuts. Let them cool on a paper towel - helps get the glaze to stick. Dip in warm glaze.