Combine yeast, 1 tablespoon of the caster sugar, 200g of the flour and 1/2 of the milk. Mix well and allow to rest in a warm place until the dough doubles its size.
Beat the whole egg, egg yolks and remaining sugar until light and smooth. Add remaining flour, milk, vanilla, lemon juice and zest, salt and vodka; mix well. Stir in prepared yeast mixture, and knead until the dough is smooth. Gradually add 6 tablespoons of oil, 2 tablespoons at a time, and knead for 10 minutes.
Preheat the oven to 40 degrees C. Place the dough inside the oven, cover with a kitchen cloth, leave the door ajar and allow to rise until doubled.
Roll out the dough so it is 2cm thick. Cut circles 4cm in diameter. Spoon 1 teaspoon jam in the centre of each circle and shape into a ball, covering the filling.
In a deep fat fryer or large, deep saucepan, heat the oil to 190 degrees C (check the temperature by adding a piece of dough, it should float immediately). Fry the doughnuts in batches on both sides until golden brown.
Place doughnuts on a piece of kitchen paper to absorb excess oil. Sprinkle with icing sugar.