Mix all filling ingredients except butter in a bowl and let soak.
Rub chilled butter into flour and icing sugar until it resembles fine breadcrumbs.
Combine egg, lemon juice, and two tablespoons of water into the flour mixture to form a dough.
Knead the dough into a ball, wrap in cling film, and chill for 15 minutes.
Preheat the oven to 180°C.
Line a 20cm pie dish with the larger portion of rolled dough and add the filling and butter cubes.
Create a lattice using eight 1cm wide strips from the remaining pastry.
Dampen the pastry edges and secure the lattice on top of the tart.
Bake for 15 minutes at 180°C, then reduce to 160°C for 20 minutes.
Beat softened butter, light brown sugar, and rum together to make the rum butter.
Serve the tart with a spoonful of the chilled rum butter.