Preheat your oven to 375 degrees F/190 degrees C/gas 5. Dust a clean surface and a rolling pin with flour and roll out your puff pastry until it's just over 1/4-inch/0.5cm thick. This will be enough to cover the ovenproof frying pan you'll be cooking the tarte Tatin in, leaving about 2 inches/5 cm extra around the edge. Put the pastry to one side for now.
Peel your apples, then halve them horizontally and use a teaspoon to get rid of the seeds and core.
Put the ovenproof pan on a medium heat and add the sugar, Calvados, vanilla seeds, and pod. Let the sugar dissolve and cook until the mixture forms a light caramel.
Once the caramel looks and smells delicious - it should be a lovely chestnut brown - add your halved apples. Carefully stir everything in the pan and cook for about 5 minutes or until the apples start to soften and you get a toffee apple vibe happening. Add the cubed butter, then lay the pastry over the top. Quickly and carefully tuck the pastry down right into the edges - it's best to use a wooden spoon so you don't touch the caramel.
Bake the tarte Tatin for about 25 to 30 minutes, or until golden, with crispy caramelly pieces bubbling up from under the edges. Take it out of the oven. To make it look like a tarte Tatin you need to turn it out, which isn't hard - but you do need to be careful with that hot caramel.
So get a serving plate or board larger than your pan and put an oven glove on to protect the arm holding the board. Put the board or plate on top of the pan, then quickly, carefully and confidently turn it out (remember you can go to http://www.jamieoliver.com/how-to and see a video of how to do this safely).
Put it to one side for a few minutes, so the caramel can cool down, then divide it up and serve with a spoonful of creme fraiche or ice cream.
NotesJust please remember never ever to touch or taste hot caramel, as it can burn really badly.
If you want to see a video of this being made, go to http://www.jamieoliver.com/how-to. It's dead simple and when you've made it once you'll have the hang of it.