Make dough: Combine flour, sugar, and salt in the bowl of a stand mixer. Add butter. Using the paddle attachment, mix on low speed until butter is smaller than pea size but not totally crumbly. Whisk egg yolk, cream, and vanilla together in a small bowl and add to flour mixture. Blend just until dough comes together and is smooth. Do not overmix--otherwise it will be tough.
Form dough into a disk. Wrap in plastic wrap and chill at least 2 hours and up to 4 days.
Form and bake tart shell: Preheat oven to 375°. Lightly butter an 8-in. tart pan with 2-in. sides and a removable bottom. Roll dough out on a lightly floured surface until about 1/4 in. thick. Roll dough up onto rolling pin, and then unroll over pan. Press dough flush against bottom of pan, into bottom corners, and then lastly, up the sides of the pan. Use your thumb to brush dough from inside to outside of edge to make it even. If you have any cracks or holes, you can patch with extra dough from the edges.
Lay a piece of parchment into pan over dough, cutting to fit as needed. Fill parchment with baking beans or pie weights.
Bake tart shell until edges are light golden brown, about 20 minutes. Carefully remove parchment with beans and transfer to a plate or a tray. Bake tart shell until center dough looks dry and is starting to turn golden brown, about 15 minutes more.
Make custard: Heat milk and cream in a medium saucepan over medium-low heat until it begins to simmer. Add vanilla bean and seeds and let sit off the heat, covered, about 30 minutes to develop flavor.
Rewarm milk mixture over medium-high heat until almost simmering. Meanwhile, mix yolks and 1/2 cup sugar in a medium bowl. Whisk in cornstarch and salt. Slowly whisk hot milk mixture into yolk mixture, 1/2 cup at a time. Pour mixture back into pan and cook, whisking constantly, until as thick as pudding, about 4 minutes. Pour custard through a strainer into a clean bowl (discard vanilla pod).
Lay a piece of plastic wrap against surface of custard to prevent a skin from forming. Chill until cold, at least 3 hours and up to 4 days.
Mix almonds, remaining 1/4 cup sugar, eggs, and custard (chilled or warm) in a medium bowl. Spread into prepared tart shell. Put one plum half, cut side up, in center of the filling and arrange remaining 5 halves around it, spacing symmetrically.
Reduce oven to 350°. Bake tart on bottom rack until filling is puffed, golden brown, and firm around the center plum when pressed, 50 to 60 minutes. Let cool completely.
Remove tart shell from pan by setting it on a can and letting the rim fall away. Carefully transfer shell, still resting on pan's bottom, to a large serving plate. Dust with powdered sugar to serve.