Step 1: 

Put flour, sugar, yeast, eggs and milk in a bowl of a mixer fitted with a hook. If using dry yeast, make sure to combine the dry yeast granules with warm milk and whisking until bubbles appear before combining with other ingredients. Mix on medium speed for 6 minutes, then scrape down the sides of the bowl. If you don’t have a mixer, knead the dough by hand for 10-15 minutes.  

Step 2:

Start the mixer again on medium speed and add the butter. Make sure everything is well incorporated. Keep mixing for 6 more minutes, until the dough has come away from the bowl and looks smooth, glossy, and elastic.

Step 3:

Place the dough in a large bowl, sprinkle the surface with flour and cover it with a tea towel. Leave to rise in a warm place until it has doubled in size, about 2 hours. Knock back or gently deflate the dough to release some of the trapped air and redistribute the yeast in the dough. Cover the bowl with clingfilm and place it in the fridge for at least 4 hours or overnight.

Step 4:

Cut the dough into 60g pieces and roll into smooth balls. Place the balls on floured baking sheets, leaving 5cm between each one. Cover with clingfilm and leave until they have doubled in size, about 2-3 hours.

Step 5:

Half-fill a deep-fat fryer with sunflower oil if you have one, or use a deep, heavy-based saucepan. Heat the oil to exactly 180C. Fry the doughnuts in batches of 3 or 4 until golden brown, about two minutes on each side. When the doughnuts are ready, place them on kitchen paper to soak up excess oil, then toss in caster sugar.  

Alternatively, you can cook the doughnuts in an air fryer. Place 2-3 doughnuts in the basket and cook for 5-6 minutes at 180C until golden brown.  

Step 6:

Once the doughnuts are cool enough to handle, make a hole with the handle of a wooden spoon and fill with your favourite jam.