Warm the milk gently with the soft butter in a pan to roughly 35°c. Pour this over the yeast to dissolve it, add the cracked eggs and egg yolk and whisk well. Then add the flour, sugar and salt and mix on a stand mixer with the dough hook attachment until a smooth, elastic dough forms. Put this mixture into 2 piping bags (this allows for space to prove, one bag may burst once the mix has proven) Allow mix to rest for at least 1 hour in the fridge.
Cooked the apples in a sauce pan until soft and blend until smooth.
Pre heat a fryer to 180°c. Cut the piping bag open (about a 1 ½cm hole) gently squeeze the mix into the fryer and using a pair of scissors cut the mix into 2cm pieces. You can cook 6-10 at a time depending on the size of your fryer. Cook for 4 minutes until golden brown, shaking throughout. Take out onto a tray lined with kitchen roll. Mix Caster sugar and some ground cinnamon for the coating and gently toss the warm doughnuts into the sugar. Put your apple puree into a piping bag and fill your doughnuts. Serve straight away with vanilla Ice-cream or a caramel dipping sauce. Enjoy!