Place the first 8 ingredients into your bread machine in the order recommended in the users manual (Mine suggests all liquid first, sugars next, flour and yeast last). Turn on and set to dough cycle setting.

Once the dough cycle is complete, turn the dough out onto a floured surface and roll out to 1/2 inch thickness. Using a floured doughnut / biscuit cutter, cut into desired shapes.

Melt butter in a saucepan over medium heat. Stir in confectioners' sugar and vanilla until smooth. Remove from heat, and stir in hot water one tablespoon at a time until the icing is somewhat thin, but not watery. Set aside.

Heat oil in a deep-fryer or large heavy skillet to 350 degrees F (175 degrees C). Slide doughnuts into the hot oil using a wide spatula. Turn doughnuts over as they rise to the surface. Fry doughnuts on each side until golden brown. Remove from hot oil, to drain on a wire rack. Dip doughnuts into the glaze while still hot, and set onto wire racks to drain off excess.