Combine 3 tablespoons milk and 3 tablespoons boiling water in a measuring jug. Reserve 1 teaspoon from the measured sugar and stir it into the liquid. Sprinkle the yeast over the mixture, stir gently, and let it stand in a warm place for 5 to 10 minutes until foamy.

Combine the flour, the remaining measured sugar, and salt in a large bowl. Cut the butter into the flour mixture until it 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.

Melt 1/3 cup butter over low heat. Stir in 2 cups confectioners’ sugar and 1 1/2 teaspoons vanilla. Gradually add up to 4 tablespoons hot water until the glaze is smooth. Dip the warm doughnut holes in the glaze and place them on a wire rack to set.