Preheat oven to 180°C. Grease and line the base of a 18cm loose bottomed tart tin.
To make the pastry, add the flour, icing sugar and butter to the bowl of a food processor and pulse until the mixture resembles coarse breadcrumbs. Add the egg and pulse again until the dough comes together. Wrap in cling wrap, then rest in the fridge for about 1 hour.
On a lightly floured surface, roll out half of the pastry until 3-4mm thick. (you can freeze the remaining pastry for up to 4 weeks). Line the tart tin with pastry, then rest in the fridge for 15 minutes
For the frangipane, cream the butter and sugar in an electric mixer until pale and fluffy. Add the eggs and egg yolk, one at a time until incorporated in the mixture. Fold in the almond meal and dark rum.
Remove the tart tin from the fridge. Brush half of the strawberry jam over the bottom of the tart, then spread the frangipane on top. Scatter over half of the berries, pressing lightly into the mixture. Bake in the oven for 30-35 until golden and cooked through. Remove from the oven and brush lightly with remaining strawberry jam. Serve with whipped cream and remaining berries.