Special equipment: 11-inch fluted tart pan with removable bottom
Preheat the oven to 400 degrees F.
In a food processor combine the flour, 3 tablespoons of the sugar and the salt. Pulse in the butter and cream cheese until the mixture resembles coarse meal. Add 3 tablespoons cold water, 1/2 teaspoon of the lemon juice, the vanilla extract and egg yolk, and pulse until a dough forms. Transfer the dough to a floured work surface and form into a ball. Wrap the dough in plastic wrap, then press down to flatten and refrigerate for 30 minutes.
Using a rolling pin on a floured work surface, roll out the dough to a large circle, about 14-inches in diameter. Carefully place the dough into an 11-inch tart pan with a removable bottom. Gently press the dough into the pan so there are no air bubbles around the edges. Roll the pin over the top of the tart to cut of the excess dough Prick the dough with a fork, and chill in freezer for 15 minutes.
Line the tart shell with foil or parchment paper and fill it with pie weights or dried beans. Bake the shell until cooked but not browned, 12 to 15 minutes. Remove the liner and pie weighs and cool the shell.
Increase the oven temperature to 425 degrees F.
In a large bowl, combine the blackberries, raspberries, cornstarch, the remaining 3 tablespoons lemon juice and the remaining 3 tablespoons sugar, and gently toss to coat. Fill the crust and bake for 10 to 12 minutes, then cool to room temperature. Remove from the tart pan before slicing.