Preheat the oven to 190°C.
Bake the pastry rectangles between two baking sheets for 10-15 minutes until golden-brown and flat.
Dredge the pear slices in 2.5 tablespoons of icing sugar and griddle for 1-2 minutes until marked.
Whisk 110ml of double cream with rum and remaining icing sugar until firm peaks form.
Whisk in the chestnut purée and fold in the chopped chestnuts.
Heat caster sugar in a pan until it dissolves and turns dark golden-brown.
Remove caramel from heat and whisk in 200ml of double cream.
Whisk the remaining 200ml of double cream in a separate bowl until firm peaks form.
Fold the cooled caramel mixture into the whipped cream.
Layer pastry with chestnut cream and pears, repeating to create three layers of pastry.
Dust with icing sugar and serve on plates with the caramel cream sauce.