For the pâte sucrée: Place butter and powdered sugar into the bowl of a stand mixer fitted with a paddle attachment. Beat on low/medium speed soft and creamy, 1-2 minutes. Add the almond flour followed by the all-purpose flour and mix for another 1-2 minutes. Crack the egg into a bowl then add to the dough and mix for 30 seconds (dough may look "broken" which is okay). Cut 1/4 of the the vanilla bean in half and scrape the seeds into the mixture and continue beating for 30 for seconds to distribute the beans. Transfer dough to a work surface and shape into a 4 by 6 rectangle, ¾-inch thick. Wrap in plastic and chill 1-1 ½ hours until firm.
Pre-heat oven to 350 degrees F.Line a sheet pan with parchment paper. Roll out the dough on a lightly floured surface and place into a 8 ¾-inch tart ring (note: there will be extra dough which you can roll out for a smaller tart). Freeze for 30 minutes.
For the almond cream: Place butter and powdered sugar into the bowl of a stand mixer fitted with a paddle attachment. Beat on low/medium speed until butter is soft and creamy. Split the remaining vanilla bean and add to the cream mixture. Crack the egg into a small bowl and add to the cream mixture. In another small bowl, mix both flours, then add to the almond cream and mix to combine. Transfer to a container and set aside.
For the tart: Spread the almond cream into the bottom of the tart shell. Cut plums into ⅛-inch wedges. Arrange a ring of plum slices, facing the same direction and each one overlapping the previous slice by about two-thirds, around the edge of the tart shell. Continue with a second ring that slightly overlaps the first. Arrange the remaining slices to fill the center of the tart. Add as many plums as you can because they will shrink when baking.Bake 1 hour until crust is browned, filling is set and plums are soft and juicy. Cool completely and serve.