Place all crust ingredients except the egg yolk, into a food processor. Pulse until it has the texture of coarse breadcrumbs. Add the egg yolk, then pulse until the mixture comes together to form a crumbly pastry. The pastry will be too soft to roll out, so scoop it out into two 10 inch tart pans and press it evenly across the bottom and sides of the pans. Rest in the freezer for at least 20 mins.
For the frangipane cream, add butter, sugar, almond extract and vanilla to a medium mixing bowl. Mix together with a wooden spoon until light and fluffy. Crack in the eggs and beat until well combined. Stir in the slivered almonds.
Preheat oven to 350 degrees. Slice plums and set aside. Pour the frangipane cream into the pie shells, dividing it evenly among the two. Arrange the sliced plums on the top of the frangipane in concentric circles. Bake for 45 minutes, until the pastry appears golden at the edges.
Let the tarts cool and dust with icing sugar before serving.
Recipe by Port and Fin at https://portandfin.com/red-plum-frangipane-tart/