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.
Separate the dough into 4 even sections. Stretch each section into a long rope that is approximately 1 inch thick. Cut approximately 1 inch pieces of the dough off the rope and roll them into balls with your hands. Then place them on a baking sheet, cover them with a cloth 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 donut holes in the oil and fry them until they are golden brown on each side (approximately 2 minutes). Work in batches so you do not over crowd the pan. After frying, move the donut holes 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 donut holes in the glaze and place them on a wire rack to cool.
Once the donut holes have cooled, they are ready to serve and enjoy!