Mix together the milk and boiling water in a large mixing bowl. Stir in the yeast and 1 tsp of the sugar. Let the mixture sit for 5 minutes to allow the yeast to activate.
In a separate bowl, stir together the melted butter, flour, remaining sugar and salt.
Mix in the egg and yeast mixture and blend until a dough is formed. Add more flour if needed. The dough should pull away from the spatula but will still be slightly tacky.
Knead the dough on a floured surface and knead the dough for approximately 4-5 minutes.
Place the dough in an oiled bowl, cover and allow the dough to rise for at least an hour until the dough has doubled in size.
Roll the dough out on a floured surface to about approximately 1/4 inch thick. Cut into donuts with either a donut cutter or cookie cutters. Let the donuts sit for 10-15 minutes while you prepare the oil.
Place vegetable oil in a large stockpot at least 3-4 inches deep. Heat the oil to 375 degrees F. Fry the donuts in the oil and fry them until they are golden brown on each side (approximately 3 minutes). Work in batches so you do not over crowd the pan. After frying, move the donuts to a plate lined with a paper towel to soak up the excess oil.
Mix together the ingredients for the glaze in a mixing bowl. Make sure that the glaze is warm. Dunk each of the donuts in the glaze and place them on a wire rack to cool.
Once the donuts have cooled, they are ready to serve and enjoy!