Make the Tart Crust:

1. Prepare the dough: In a food processor, pulse together flour, powdered sugar, and salt until combined. Add the cold butter cubes and pulse 10-12 times until the mixture resembles coarse crumbs with some pea-sized butter pieces remaining. Add the egg yolk and vanilla, then pulse until the dough just begins to come together. If the dough seems too dry, add ice water, 1 teaspoon at a time, pulsing between additions.
2. Chill the dough: Turn the dough out onto a clean surface and gently knead it 2-3 times until it comes together into a cohesive ball. Flatten into a disc, wrap tightly in plastic wrap, and refrigerate for at least 1 hour (or up to 2 days).
3. Roll out the dough: On a lightly floured surface, roll the chilled dough into an 11-12 inch circle, about ⅛-inch thick. Carefully transfer it to your tart pan by rolling it around the rolling pin, then unrolling it over the pan.
4. Form the tart shell: Gently press the dough into the bottom and up the sides of the pan. Trim excess dough by rolling your rolling pin across the top of the pan. Prick the bottom all over with a fork. Freeze for 15 minutes.
5. Blind bake: Preheat oven to 375°F (190°C). Line the frozen tart shell with parchment paper and fill with pie weights or dried beans. Bake for 15 minutes, then carefully remove the parchment and weights. Bake for another 10-12 minutes until the crust is golden brown. Cool completely on a wire rack.

Make the Pastry Cream:

6. Heat the milk: In a medium saucepan, heat the milk and ¼ cup of the sugar over medium heat until it just begins to steam and small bubbles form around the edges. Do not let it boil.
7. Prepare the egg mixture: While the milk heats, whisk together the egg yolks, remaining ¼ cup sugar, and cornstarch in a medium bowl until smooth and pale yellow.
8. Temper the eggs: Slowly pour about ½ cup of the hot milk into the egg mixture while whisking constantly. This tempers the eggs so they don’t scramble. Pour this mixture back into the saucepan with the remaining milk, whisking constantly.
9. Cook the cream: Cook over medium heat, whisking constantly, until the mixture thickens and comes to a boil. Let it boil for 1 minute while whisking (this cooks out the cornstarch taste). Remove from heat.
10. Finish the cream: Whisk in the vanilla bean paste and butter until smooth. Strain the pastry cream through a fine-mesh strainer into a clean bowl to remove any lumps. Press plastic wrap directly onto the surface of the cream to prevent a skin from forming. Refrigerate until completely cold, at least 2 hours or overnight.
11. Lighten the cream: When ready to assemble, whip the cold heavy cream to stiff peaks. Whisk the chilled pastry cream until smooth, then fold in the whipped cream until fully combined. This creates a lighter, mousse-like filling.

Assemble the Tart:

12. Fill the tart: Spread the lightened pastry cream evenly into the cooled tart shell using an offset spatula. Smooth the top.
13. Arrange the berries: Starting from the outer edge, arrange raspberries in concentric circles over the pastry cream, placing them close together. You can stand them on their flat ends or lay them on their sides for different looks.
14. Make the glaze: In a small saucepan or microwave-safe bowl, heat the apricot jam, lemon juice, and water until melted and smooth. Strain through a fine-mesh strainer to remove any fruit chunks.
15. Glaze the tart: Using a pastry brush, gently brush the warm apricot glaze over the raspberries. This adds shine and helps preserve the berries.
16. Serve: Refrigerate the tart for at least 30 minutes before serving to let everything set. Remove the outer ring of the tart pan just before slicing. Serve chilled.