Preheat the oven to 200C/400F/Gas 6.
Roll the puff pastry out on a clean work surface to a large sheet, 3mm thick. Using a bowl or plate, cut a circle about 25cm/10in in diameter. Crimp the edge before turning the whole sheet over and laying it directly onto a flat baking tray. Chill in the fridge for at least 10 minutes.
Remove the pastry from the fridge and spread the apple compôte all over the base of pastry, leaving a 1cm/½in border at the edge.
Slice the apples the thickness of a two-pound coin and place them onto the pastry sheet, fanning them out, starting from the outside and working in. The apples should overlap each other. Use the largest slices on the outside and place the smallest slices in the middle of the tart.
Once all the apples have been laid out, sprinkle over the caster sugar and dot with the cubed butter. Brush the border with the beaten egg and bake in the oven for about 30 minutes, or until golden-brown and risen around the edge.
For the Chantilly cream, whisk the cream, icing sugar and seeds from the vanilla pod in a bowl until very soft peaks form and set aside until ready to serve.
When ready to serve, place the tart onto a serving plate. Warm the calvados in a small saucepan. Ignite the alcohol with a match (be careful of your fingers) and pour over the tart. Serve with Chantilly cream.