In a large measuring jug, combine milk and boiling water. Add a teaspoon of sugar and the yeast. Stir gently, then leave in a warm place to activate.
In a mixing bowl, combine flour, remaining sugar, and salt. Cut in butter until it resembles crumbs.
Add beaten egg and yeast mixture to flour. Mix into a smooth dough (~5 minutes).
Knead dough on a lightly-floured surface for 5-10 minutes. Let it rise in a covered bowl for 1 hour.
After rising, divide dough into 4 pieces. Stretch each into a rope and cut into 1-inch strips. Roll into balls and set aside.
Heat oil to 375°F. Fry doughnuts until golden brown (~2 minutes per side).
Drain and glaze while warm.