How to Make It
In a food processor, pulse both flours with the cornmeal, sugar and salt. Add the butter and pulse until the mixture resembles coarse meal with some pea-size pieces of butter still visible. Sprinkle the ice water over the mixture and pulse until the dough just starts to come together; you should still see small pieces of butter. Scrape the dough out onto a work surface and gather it together. Quarter the dough and form into four 1/2-inch-thick disks. Wrap the disks in plastic and refrigerate until well chilled, at least 1 hour.
In a large saucepan, melt the butter. Add 1/3 cup of the sugar and the vanilla seeds and cook over moderately high heat, stirring constantly, until the sugar turns light amber, about 1 minute. Add the apples and lemon juice and cook, stirring occasionally, until all of the liquid has evaporated and the apples begin to caramelize, 11 minutes. Transfer to a bowl to cool, then stir in the plums.
Preheat the oven to 400°. On a lightly floured work surface, roll out each disk of dough to a 6-inch round, a scant 1/4 inch thick. Transfer the rounds to 2 baking sheets lined with parchment paper. Mix the remaining 2 tablespoons of sugar with the flour and sprinkle evenly in the center of the dough rounds. Spoon the apple-plum filling over the dough, leaving a 1 1/2-inch border. Fold the dough border over the filling, leaving the centers exposed. Lightly brush the tart rims with water and liberally sprinkle them with sugar.
Bake the tarts for about 35 minutes, until the crust is browned and the filling is bubbling. Let cool slightly on the baking sheets, then transfer the tarts to a rack and let cool completely, at least 30 minutes. Serve with crème fraîche or vanilla ice cream.