In a food processor, combine the flour, icing sugar, and cold butter. Add the egg yolk, vanilla extract, and 1 tablespoon of water. Process until the mixture forms a crumbly, uniform dough.
Transfer the dough to a lightly floured work surface, shape it into a ball, then flatten it into a disk. Wrap it in plastic wrap and refrigerate for 30 minutes.
Preheat the oven to 355°F (180°C).
Roll out the dough to fit a removable-bottom tart pan. Press the dough into the pan and trim any excess. Prick the bottom of the crust with a fork.
Refrigerate the crust for 20 minutes. Line it with parchment paper and fill it with dried beans or pie weights.
Bake for 15 to 20 minutes, or until the edges are lightly golden.
Remove the parchment paper and the dried beans or pie weights, then continue baking for another 15 minutes, until the crust is golden brown. Transfer to a wire rack and let cool completely.
For the filling, set aside 500 g of the fresh raspberries.
Place the remaining raspberries and the icing sugar in a blender or food processor and blend until smooth. Spread the raspberry purée evenly over the cooled tart crust, then arrange the reserved whole raspberries on top.
In a small saucepan, gently heat the apricot jelly until melted. Strain it through a fine-mesh sieve to remove any large pieces of apricot. Using a pastry brush, lightly glaze the raspberries with the warm apricot jelly.
Serve and enjoy!