Cream egg yolks and eggs with sugar and lemon peel (zest), add the leaven, flour, milk, salt, rum, and mix.
When all ingredients are combined, add gradually melted butter, knead, set aside to rise.
When the dough doubles in bulk, divide into 4 parts. Roll out each part on floured board to 1/3" thickness.
Drain excess liquid from the jam.
Cut rounds with small cookie cutter, place a bit of jam in center, cover with another round, pinch together with fingers, and then cut out again with cookie cutter (even the sides)
Place the doughnuts on flour sprinkled board, leave space between each, cover with a towel and allow to rise.
Put up fat for frying, test fat for temperature with a piece of dough. If dough floats to the top immediately, the fat is correct temperature.
Brush flour off of the leavened doughnuts, place in hot fat, upper part down, the doughnuts should be able to float freely in the fat.
When half the doughnut is browned, turned over and fry.
Removed with a 2-tine fork onto absorbent paper; when drained, place on a platter, sprinkle vanilla sugar.