Roll the pastry out to line a 27cm/11in tart tin. Prick the base, then chill for at least half an hour.
Blind bake the pastry for 12 minutes by lining the pastry with clingfilm and weighting with dried beans.
Remove the beans and the cling film and bake for another eight minutes to dry out.
Slice the top and the base of the pineapple, and cut it into eight long wedges, from top to bottom.
Cut the tough core out of each wedge, then slice the wedges. Melt the butter in a frying pan until foaming.
Add the pineapple pieces and fry for about three minutes. Then sprinkle over 80g/3oz sugar, and pour in the rum.
Stir, allow to heat briefly, then slowly tilt the pan towards the flame, or light with a match. Let the flames flare up then die down. Cook for 3-4 mins longer until the juices are reduced to a thick rich syrup.
Cool slightly, then lift the pineapple out and arrange in the pastry case. Reserve the syrup.
To make the filling, whisk the mascarpone with all the filling ingredients, including the last of the sugar and the syrup left from the pineapple.
Pour over the pineapple. Bake for about 25 minutes, until the filling has just set.