Pączki: Rich Polish Jam-Filled Doughnuts

Wake up the yeast. Stir the yeast and 1 tsp of the sugar into the lukewarm milk and leave for 5-10 min until foamy on top.

Beat the yolks. Put the yolks, whole egg and the rest of the sugar in the mixer bowl and whisk for 3-4 min until thick and pale. Mix in the vanilla, salt and the yeasty milk. Beating air into the yolks lightens this heavy dough.

Knead with the butter. Fit the dough hook, add the flour and knead on low for 5 min. Add the soft butter a spoonful at a time, then knead on medium for 10-12 min until glossy, very soft and coming away from the sides. The long kneading builds the structure needed to hold all that fat.

First rise. Shape into a ball, put it in the oiled bowl, cover and leave somewhere warm for about 1.5 h until doubled.

Second rise. Knock out the air, fold the dough over on itself a few times, cover again and leave for 30 min.

Cut and prove. Roll the dough out on a floured worktop to 1.5 cm thick and cut rounds with the cutter, rerolling the scraps once, to make 16. Set them on the floured trays, cover loosely and prove for 30-45 min until visibly puffy.

Fry. Heat 2.5 cm of oil in the heavy pot to 175 °C. Fry 3 at a time for 2.5-3 min on each side, until a deep chestnut brown with a pale band around the middle; adjust the heat to stay between 170 and 180 °C. Drain on the paper. The centre of one should reach about 88 °C, or break it open to make sure the inside is cooked.

Fill with jam. When cool enough to handle, make a hole in the side of each with the skewer. Pipe in about 1 tbsp jam until it just shows at the opening, and dust with icing sugar if you like.