PREPARE THE YEAST: Heat the milk in a small saucepan until just warm (but not hot!) when you dip your little finger into it. Remove from the heat, then stir in the yeast. Set aside.

MAKE THE DOUGH: In the bowl of a stand mixer with the dough hook fitted (see note 1) combine 175g flour, sugar, vanilla and salt. While mixing, add the butter and egg yolk, then give the milk and yeast mixture a stir and pour it into the bowl. Run the mixer on high until the ingredients are combined, then with the mixer on low add the remaining flour. Knead for 5 minutes.

After 5 minutes the dough should be moving freely around the bowl of the mixer, and only lightly sticky. If it is still a little liquid or sticking to the sides of the bowl add one tablespoon of flour and knead for another minute.

LET THE DOUGH RISE: When the dough has finished kneading, shape it into a ball - it should feel soft, springy and elastic. Place it back in the bowl, cover with a clean cloth or some clingfilm and allow to rise in a warm place for 1 hour. 

DIVIDE THE DOUGH: When the dough has risen, turn it out onto the bench top. Flatten out the air and divide into eight. I find it useful to weigh the dough so that my pieces are as even as possible.

SHAPE AND SECOND RISE: Roll each into a tight ball, place on a lightly floured tray, then cover again and allow to rise for another 20 minutes.

PREPARE TO COOK: Meanwhile fill a large, heavy-based saucepan (enamelled cast iron is ideal) with the oil or shortening, line a plate with paper towel and stir together the topping sugar and spices on a small plate.

HEAT THE OIL: When the dough has risen again, heat the oil to 160°C /320°F. (See notes) Gently take one of the balls of dough, pinch a hole in the middle with your index finger and thumb, and gently stretch the hole in the middle to about 5cm in diameter.

COOK: Carefully lower into the hot oil, then repeat until the pan is full but not crowded - I cook five or six at a time. Cook the donuts until golden brown on the underside, around 1 minute. 

TURN THE DONUTS: Turn carefully using a slotted spoon and cook until golden brown on the other side, then lift out to the paper towel lined plate to drain, before pressing the donuts into the sugar and spice mixture while still warm.

SERVE: Repeat with the remaining dough, until finished, keeping an eye on the temperature of the oil. Serve warm.