Method

 For the filling:

1 Roughly chop the apples and set aside.

2 Make the caramel apple puree filling by putting the sugar in a medium sized saucepan on a low heat. Slowly begin to cook the caramel, shaking the pan a little to help it cook evenly. Refrain from stirring the sugar. Once the caramel has turned an even golden brown throughout, add the butter, taking care as the caramel will spit and splatter a little.

3 Swirl the pan to melt the butter, add the salt, cider or Calvados, vanilla and the apples, and continue to cook on a low heat for about 15 minutes until the apples are soft.

4 Remove the caramel from the heat and leave to cool completely. Put the caramel apples into a food processor and blend to a smooth puree. Set aside.

5 Make the custard by mixing the custard powder with a little of the 375ml milk and whisking to a smooth paste. Put the remaining milk into a medium saucepan and bring to a simmer. Add the custard powder paste and whisk together. Cook the custard until thick, smooth and glossy. Set aside to cool.

For the dough:

1 Put the flour, salt, sugar and yeast into a mixing bowl of a mixer fitted with a dough hook attachment.

2 Place the milk and water into a saucepan and gently heat until warm but not hot. Whisk the eggs and butter together in a separate bowl, and slowly whisk in the warm milk, mixing well to combine. Begin to mix the dry ingredients in the mixer on a low speed. Slowly add the liquid egg mix and continue to mix on a medium speed for about 10 minutes, until smooth and elastic.

3 Transfer the dough to a lightly oiled bowl and cover with clingfilm. Leave to rise in a warm place for one hour or until doubled in size. Alternatively, place in the fridge overnight.

4 Once risen, tip the dough out onto a lightly floured work surface and knock the dough back, pushing down to release any air bubbles. Work the dough for 2-3 minutes until smooth and elastic.

5 Preheat the oven to 190 degrees and grease a 12-hole muffin tin.

6 To finish the filling, beat the apple puree into the cool custard until smooth.

7 Divide the dough into two pieces and roll each out to a rough 30cm x 20cm rectangle. Divide the caramel apple custard between the two rectangles, spreading evenly, leaving an inch around the edges. Roll up each rectangle from the long end to form a log. Cut each log into six using a sharp knife and arrange the slices in the muffin tin. Cover the tin with clingfilm or a tea towel and leave to rise again for 30 minutes.

8 Mix the egg and milk to make an egg wash and brush over the top of each bun. Bake for 30 minutes until golden and cooked through. Cool before removing from the tin.

9 To make the icing, sift the icing sugar into a bowl and add the Calvados. mixing well to combine. Drizzle over the buns and serve.