Pre-heat the oven to 180 degrees celsius. Soak the sultanas in the rum for at least 10 minutes.
Gently melt 55g of the butter in a big frying pan with half the sugar until it is just starting to caramelise. Add the bananas, pecan nuts and sultanas and cook gently in the pan for 2 minutes. Take off the heat and leave to cool on the side, leaving the mixture to set slightly.
Take one sheet of filo pastry and lay it out until it is about 40cm long. Melt another 55g of the butter and use some of it to brush the filo pastry all over. Roll out another sheet and place on top of the first sheet. Brush with butter and then repeat with a third sheet.
Place the banana mixture as a cylinder at the bottom of the pastry. Fold the edges over and roll it up. Place the strudel on a greased baking sheet, seam side down. Brush it all over with the rest of the melted butter and sprinkle with the icing sugar and cinnamon. Bake in the oven for 20-25 minutes, then leave to cool slightly before serving.
For the sauce, melt 85g of butter with the remaining Demerara sugar and heat until thickened and the sugar is dissolved. Stir in the cream, bring to the boil, remove from the heat and set to one side. Serve two slices of strudel per portion, pour over the sauce and add a dollop of vanilla ice cream.