For the dough, warm the milk and 90ml/3fl oz water in a small saucepan until lukewarm.
Place all the other ingredients, except the butter, in the bowl of a freestanding mixer with a dough hook attachment, making sure the yeast doesn’t touch the salt. Add three-quarters of the milk and water mixture.
Start the mixer on a low speed until all the ingredients are incorporated. Add a bit more liquid if the dough seems too dry; you want a slightly sticky dough. Increase the speed and mix for seven minutes.
Spread the dough out onto a baking tray lined with baking parchment. Cover with cling film and place in freezer to cool.
Using a rolling pin, flatten the butter out between two pieces of baking parchment into a rectangle 33x19cm/13x7½in and place in the freezer.
After 15 minutes remove the dough from the freezer and roll it out to a rectangle 50x20cm/19½x8in. With a short edge towards you, place the flattened butter on the lower two-thirds of the dough.
Fold the top third of dough over the butter and then fold the bottom third upwards so all the butter is encased. Press the edges firmly together.
Turn the block of dough 90 degrees and roll out to 50x20cm/19½x8in. Fold the top third down and the bottom third up and place back in freezer for 15 minutes.
Repeat the rolling and folding twice more, placing the dough in the freezer for 15 minutes in between. Store covered in the fridge until ready to use.
Meanwhile, for the filling, chop the apple into 5mm chunks and place in a large heatproof bowl. Add the lemon zest, mixed spice, butter, raisins, walnuts and sugar.
Cover with cling film and place in a microwave on the highest setting for six minutes (you could also do this in a saucepan, cooking until the apples are softened). Stir to combine, then spread the filling out on a plate to cool completely.
Cut the pastry into two equal pieces and roll out one half on a well-floured work surface to a thickness of 4mm.
Using a 11cm/4½in round cutter, cut out six circles. Place a tablespoon of the apple filling in the centre of each circle and sprinkle a little Cheshire cheese on top. Season with pepper.
Brush a little beaten egg around the edge of each circle of pastry. Fold in half to enclose the filling and press to seal.
Place each pastry on a baking tray lined with non-stick baking paper. Repeat the rolling, cutting and filling process with the second batch of dough to make 12 chaussons. Cover the chaussons with cling film and allow to prove at room temperature for 40 minutes.
Preheat the oven to 200C/400F/Gas 6. (Do not use a fan-assisted oven.)
Make three cuts in the top of each chausson to allow steam to escape and brush with beaten egg. Bake for 20 minutes, or until well risen and golden-brown.
Remove from the oven and allow to cool slightly before transferring to a cooling rack.