Heat the milk to a temperature of 36-40 °C. Melt the butter and cool slightly.
First, prepare the dough: mix 50 g of warm milk with 1 teaspoon of sugar, add live yeast and leave in a warm place for 10 - 15 minutes, covered with a lid or kitchen towel.
Beat the eggs with the remaining sugar, pour in the butter, yeast dough, warm milk, vanilla sugar and mix. Knead the dough, adding flour in parts.
Dust the dough with flour and roll out a circle 1.5-2 cm thick, then cut it into circles (you can use a glass with a diameter of 6 cm). Leave the circles for 30 minutes in a warm place to rise. Fry the donuts in well-heated oil and place on paper napkins. Let cool slightly and fill with jam using a pastry syringe.
Serve sprinkled with powdered sugar. You can also use coconut flakes, condensed milk or chocolate icing for decoration.