Time: 50 minutes
Preheat the oven to 200C/Gas 6.
Roll out the puff pastry into a small rectangle about 15x20cm. Cut the rectangle into 4 equal pieces and lay them onto a baking tray lined with baking parchment. Cut a criss cross into the pastry for decoration.
Mix together the egg and milk and brush this over the puff pastry. Sprinkle over the grated cheese and a little pepper and bake in the oven for 20 minutes until risen and golden.
Meanwhile, set a large shallow sauté pan over a low heat and add the butter and oil. When the butter has melted, add the shallots, potatoes and carrots and fry them gently for 5 minutes until the shallots have softened.
Pour over the cider and bring the liquid to the boil. Leave to simmer for about 10 minutes, with a lid on until the potatoes are soft.
Add the rest of the vegetables, cream and tarragon and season with salt and pepper. Simmer for a couple of minutes until the vegetables are just cooked.
Serve straight away with the puff pastry top.