In a large measuring jug, combine the milk and boiling water. Add a teaspoon of the sugar and the yeast. Stir gently, then leave it in a warm place for the yeast to activate (form foam).
In a large mixing bowl, combine the flour, the rest of the sugar, and the salt. Cut in the butter using your fingers or a pastry blender, until it resembles crumbs.
Add the beaten egg and yeast mixture to the flour mix, and mix into a smooth dough (about 5 minutes of mixing).
Turn the dough out onto a lightly-floured counter and knead for about 5 to 10 minutes—it should feel springy and little bubbles should form under the surface. Place it back in the bowl, cover with a cloth or plastic wrap, and let rise for about an hour until double in size.
Once risen, place the dough onto the counter and cut it into 4 pieces. One piece at a time, stretch it into a long rope about an inch to an inch and a half wide. Cut strips about an inch long, ball them up with your hands, and place them on a baking tray or wire rack to wait.
Cover the doughnuts holes with a cloth to rise while you heat the oil to 375°F.
Place the doughnuts into the oil and fry until golden brown on each side, about 2 minutes. Be sure to fry only a few at a time so they don’t overcrowd and stick together.
Drain on a paper towel or wire rack over a cloth, before glazing them. Be sure to glaze them warm, or else they won’t get that delicious coverage!