Warm up the milk (but don’t boil it as hot milk will kill the yeast), pour it into a 1l container; add crumbled yeast, 1 tbsp flour and 1 tbsp sugar. Stir and put to a bigger pot with very warm water in it. Leave the mixture for 15 minutes to rise and get foamy.
Sift the rest of the flour to a big bowl, add salt and vanilla sugar.
Beat the egg, egg yolks and 2 tbsp of sugar with electric mixer for 10-15 minutes.
Melt the butter.
Pour the foamy yeast mixture to the bowl with flour, stir with a wooden spoon. Add the beaten eggs and stir again.
Hand knead the dough very well for 15-20 minutes (you can do it with the mixer instead, it will take you then 10-15 minutes). At the end of this process, the dough shouldn’t stick to your hands anymore.
Add the melted, cooled down butter and the spirit; knead until all the ingredients are combined. Cover the bowl with a tea towel and keep in a warm place for 1-1.5h till the dough increases its volume considerably.
Dust a working surface with a bit of flour and knead the risen dough for 2-3 minutes to eliminate air bubbles.
Flatten the dough to approx. 2 cm (with your hands or a rolling pin) and cut circles (6-7cm diameter). Form a ball with the leftover dough, flatten it and cut the rest of the circles using up all the dough.
Place the circles on a flour dusted surface, cover with a tea towel and keep in a warm place for 30-45 minutes.
If you prefer to fill the doughnuts before frying them, flatten each circle, put 1 tsp of your chosen jam in the middle and stick the edges together tightly forming a ball. If you are planning to fill the doughnuts after you fry them, transfer the jam to a pastry bag fitted with a long and sharp tip.
Begin heating up the oil on a medium heat 15 minutes before you are planning to start frying the doughnuts. It works the best if the oil heats up slowly and for a long time, in a big and wide pan. The oil is ready when it reaches temperature 180C.
Make the lemon icing by mixing the icing sugar with the lemon juice.
Gently slip the risen doughnuts to heated oil (you shouldn’t fry more than 4-5 doughnuts at a time as you don’t want to decrease the oil temperature rapidly), fry for 2 minutes, turn over and fry for 2 minutes on the other side. When done, take them out from the oil with a slotted spoon and place on a plate covered with paper towel. Repeat with the rest of the doughnuts.
If you are filling them at this stage, start with the doughnuts you fried as the first ones (they will have cooled down a bit by now). Take one, press the tip of the pastry bag deeply and squeeze the desired amount of jam. Repeat with the rest.
Cover the doughnuts with icing or if you prefer simply dust them with icing sugar.