Combine 3 tablespoons of milk with 3 tablespoons of boiling water in a measuring jug. Stir to mix. Add 1 teaspoon of sugar and stir to dissolve. Sprinkle 1 teaspoon of yeast over the liquid and stir gently. Let sit for 5-10 minutes in a warm place until foamy.

In a large mixing bowl, combine flour, sugar, and a dash of salt. Cut cold butter into the flour mixture using fingers or a pastry blender until the texture resembles coarse crumbs.

Make a well in the center of the flour mixture. Pour in the activated yeast mixture and beaten egg. Mix until a soft dough forms. Adjust with more flour if too sticky or milk if too dry.

Turn the dough onto a floured surface and knead for 5-10 minutes until smooth and elastic. Place in a greased bowl, cover, and let rise in a warm place for 1 hour or until doubled in size.

Turn the risen dough onto a floured surface. Divide into four sections, roll each into a 1-1.5 inch rope, and cut into 1-inch pieces. Shape into balls and let rise for 15-20 minutes.

Heat 3-4 inches of oil in a wok or deep fryer to 375°F (190°C). Maintain this temperature for even frying.

Carefully place doughnut balls into the hot oil in batches. Fry each side for 1 minute or until golden brown. Remove with a slotted spoon and drain on paper towels.

In a saucepan, melt butter over low heat. Stir in confectioners' sugar and vanilla extract. Gradually add hot water until the glaze is smooth. Dip warm doughnuts into the glaze and place on a wire rack to set.