Preheat the oven to 400°F (200°C), Gas mark 6. Unroll the pastry on a clean surface and carefully cut into around, 1in (2.5cm) larger than a 9-10in (22-25 cm) ovenproof frying pan or heavy-duty shallow cake tin (not a loose-based one). Place on a baking sheet lined with parchment paper and chill for at least 30 minutes.
Meanwhile, peel, core and quarter the apples and toss them in half of the lemon juice. Mix the butter with the vanilla seeds then spread evenly into the frying pan. Sprinkle over the caster sugar and then arrange the apple quarters tightly on top, cut-side up. Cook over a medium to high heat for 15 minutes or until the apples are caramelised, cooked through and light golden brown, being careful that they don’t stick on the bottom. Remove from the heat, then sprinkle the apples with the lemon rind and the rest of the lemon juice. Leave to cool for 5 minutes.
Lay the chilled pastry sheet over the top of the apples, tucking in the edges and turning them down so that when the tart is turned out, the edges will create a rim that will hold in the caramel and apple juices. Bake for 25-30 minutes until the pastry is crisp and golden brown and the apples are completely tender but still holding their shape.
Leave the tart in the tin for a minute or two, then loosen the edges with a palette knife and turn upside down onto a flat plate. Rearrange any apples, which have loosened back into place with the palette knife and leave to cool for a few minutes. This enables all the juices to be reabsorbed and allows the caramel to set slightly because of the pectin in the apples.
To serve the apple tarte tatin, cut into slices and serve on slightly warmed plates with a dollop of the whipped cream.