Heat the oven 200C/fan 180C/gas 6. Roll the pastry out to ½cm thickness, cut out a circle approximately 26cm, then prick all over with a fork. Lay a sheet of baking paper on a solid baking sheet and put the pastry on top. Chill in the fridge while you make the sauce and frangipane filling.
To make the butterscotch
Put the sugar and butter in a pan and heat gently until the sugar has dissolved. Stir in the cream, then increase the heat and simmer for 2 minutes, stirring all the time. Take off the heat and stir in the vanilla and a big pinch of salt.
To make the frangipane
Beat the butter, then mix in the icing sugar, almonds and flour. Add the egg and mix it in. Spread the frangipane over the pastry, going right to the edge, then put it in the fridge.
To make the tart
Peel, quarter and core the apples, then slice them as finely as possible. Arrange the apple slices on top of the tart so they overlap and fan out from the centre of the tart, completely covering the pastry.
Cover the apples with baking paper and put another baking tray on top to keep the apple slices flat while cooking. Bake for 15 minutes, then remove the top tray and baking paper and cook for another 30 minutes, or until the pastry is crisp underneath.
Take out and brush with just enough butterscotch to cover the surface in a thin layer. Put back in the oven for 5 minutes.
Leave to cool for 10 minutes before serving with the rest of the sauce.