Make the Tart Shell: In a standing mixer fitted with the paddle, blend the almond paste, sugar and salt with 3 tablespoons of the butter at medium speed until smooth. Beat in the remaining butter. Add 2 cups of flour and beat at low speed until just combined, then beat in the egg and milk. Scrape the dough onto a piece of plastic wrap and flatten into a disk. Wrap tightly and refrigerate for 2 hours, until very firm.
Preheat the oven to 350°. On a lightly floured work surface, roll out the dough to a 14-inch round, 1/4 inch thick; transfer to a 12-inch fluted tart pan with a removable bottom, pressing over the bottom and up the side without stretching. Trim any excess dough. Freeze the shell for 15 minutes.
Line the shell with foil and fill with pie weights or dried beans. Bake for 35 minutes, until the pastry is firm and starting to color. Remove the foil and weights and bake the shell for another 20 minutes, until golden and cooked through. If the rim starts to browns too quickly, cover with foil. Transfer the tart shell to a rack; let cool.
Meanwhile, Make the Filling: In a medium saucepan, combine the milk with the vanilla bean and seeds and half of the sugar. Bring to a simmer over moderate heat, stirring. Remove from the heat. Remove the vanilla bean and reserve for another use.
Fill a large bowl with ice water. In a medium heatproof bowl, whisk the eggs with the cornstarch and the remaining sugar until smooth. Gradually whisk in half of the hot milk. Pour the mixture into the saucepan and bring to a boil over moderate heat, whisking constantly, until the pastry cream is thickened, 3 minutes; scrape into a stainless steel bowl. Set the bowl in the ice bath and let stand, stirring often, until the pastry cream has cooled completely.
Spread the pastry cream in the shell in an even layer. Arrange the apricot quarters in four concentric circles, leaving a 1-inch gap between the second and third circles and a 2-inch round in the center of the tart. Fill in the spaces with the blueberries. Bake the tart for 50 minutes, until the apricots are tender. Let cool slightly. Unmold the tart, cut into wedges and serve warm or at room temperature.