In a medium bowl, add the milk, sugar, and yeast, stirring to combine.

In a separate medium bowl, add the butter, eggs, and vanilla extract, stirring to combine.

Add the milk mixture to the egg mixture and whisk to combine. Transfer to a large bowl and add the flour in thirds, stirring between each addition.

Dump the dough onto a lightly floured surface and knead for 5 minutes, until smooth. Gently poke the dough with a finger--the dough should bounce back up from the indentation.

Place the dough in a large bowl, and lightly coat the dough with oil. Cover the bowl with plastic wrap.

Let the dough rise in a warm place for an hour, or until doubled in size.

Take the dough out and knead on a floured surface for 5 minutes until smooth. Place the dough in an oiled bowl and repeat with rise overnight in refrigerator.

Roll out the dough on a floured surface until ¼ inch (6 mm) thick.

Cut out the doughnuts and donut holes with a cookie cutter and piping tip.

Melt enough shortening over medium heat to come up just 2 inches (5 cm) up on the side of a heavy frying pan. Heat the shortening to 375°F (190°C)

Fry the donuts and donut holes for 45 seconds on each side, or until golden brown.

In a bowl, combine the powdered sugar, dry milk powder, vanilla extract and hot water until smooth.

Strain the glaze through a fine-mesh sieve to remove any lumps.

Dunk the donuts in the glaze or drizzle the glaze on top.