To make the pastry, combine the flour, icing sugar, butter and vanilla paste in the bowl of a food processor and pulse until the mixture resembles rough breadcrumbs.
With the motor running. add the egg yolks and just enough water for the dough to come together in a ball.
Remove the dough from the food processor and shape into a disc. Wrap in cling film and place in the fridge for 30 minutes.
After 30 minutes, roll the dough out on a floured surface and place in a suitable tart case.
Place back in the fridge while you get started on the filling. Pre-heat the oven to 180°c.
In the bowl of a mixer, cream together the butter and caster sugar until light and fluffy.
Add the vanilla paste, almond essence and eggs and beat well, scraping down the bowl if necessary.
Add the ground almonds and flour and mix until well combined.
Spread the almond mixture onto the prepared pastry and top with the sliced plums.
Place the tart in the oven and allow to bake for 20-25 minutes until the frangipane is golden brown and cooked.
Remove from the oven and allow to cool before slicing and serving.