Preheat the oven to 180 °C. Roll out the shortcrust pastry to fit a 25 or 30 cm removable-bottom tart pan.
Line the tart pan and prick the dough at least 7-8 times with a fork. Bake the crust until golden, about 10-12 minutes. Set aside.
Chop 250 grams of white chocolate and place it in a heatproof bowl.
In a medium saucepan, scald 250 grams of whole milk, 250 grams of heavy cream, and 90 grams of granulated sugar over medium-high heat.
Scrape the seeds from ½ vanilla bean and add them along with the pod to the pan.
While the milk heats, whisk together 2 large eggs and 2 large egg yolks with 2 tablespoons of cornstarch until smooth.
Gradually whisk the hot milk into the eggs, then return the mixture to the heat. Cook on low heat, stirring constantly, until it begins to boil and thickens.
Remove from heat. Immediately strain the pastry cream over the chopped chocolate and let sit for 2-3 minutes.
Gently mix until smooth and all white chocolate pieces are melted.
While still warm, pour the filling into the baked tart shell and level it to form an even layer.
Arrange 700-900 grams of fresh blackberries in concentric circles on the filling.
Let the tart cool for at least 2-3 hours until the filling has set.