Combine warm milk, yeast, 1 teaspoon sugar, and 5 tablespoons flour. Cover and let rise for 10–15 minutes.
Melt butter and allow it to cool slightly.
Whisk egg yolks, whole egg, and remaining sugar in a heatproof bowl over gently simmering water for approximately 10 minutes until pale and fluffy.
Combine remaining flour, yeast starter, and egg mixture.
Knead while gradually adding melted butter. Add vodka or rum and knead until elastic.
Cover and rise for 40–60 minutes, until doubled.
Roll dough to approximately 1 cm thick and cut 7 cm circles.
Fill half the circles with thick jam and cover with the remaining circles. Seal edges.
Cover and rise for approximately 30 minutes.
Heat oil to 350°F. Fry donuts in batches for approximately 2 minutes per side, until golden and cooked through.
Drain on a wire rack.
Mix powdered sugar with hot water to make a glaze.
Glaze the warm donuts and decorate with candied orange peel if desired.