Slice the top off the apple, chop the flesh from this part and place it into a bowl, discarding the rest of the top part. Then cut out as much flesh as possible from the main part of the apple, leaving the outer shell intact. Discard the core, chop up the flesh and add this to the bowl.
Melt half of the butter in a small ovenproof frying pan, place the apple flesh into the pan and cook gently for 4-5 minutes, or until softened to a purée.
Transfer the apple purée to a bowl and leave to cool for five minutes.
Melt the remaining butter in the pan. Place the apple shell into the pan, sprinkle brown sugar over it and transfer to the oven to bake for 5-6 minutes, until beginning to soften and turn golden-brown.
Meanwhile, place the whisked egg whites into the bowl with the apple purée and fold together, then fold in the Cheshire cheese.
Remove the apple from the oven, spoon the purée mixture inside it and return to the oven for 5-6 minutes, or until puffed up and golden-brown.
To serve, transfer the baked apple to a serving plate.