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1. In a large mixing bowl, combine the all-purpose flour and powdered sugar. Whisk until well blended.
2. Incorporate the softened unsalted butter into the flour mixture using fingers or a pastry cutter until it resembles coarse crumbs.
3. Add the egg yolk and mix gently until just combined.
4. Gradually add cold water, one tablespoon at a time, mixing until the dough forms a ball. Avoid overworking the dough.
5. Wrap the dough in plastic wrap and refrigerate for at least 30 minutes.
6. Wash the fresh raspberries gently and let them drain in a colander.
7. In a medium saucepan, combine granulated sugar, cornstarch, lemon juice, and vanilla extract. Stir until mixed, then fold in the raspberries.
8. Cook the raspberry mixture over medium heat, stirring gently, until it thickens slightly (about 5-7 minutes). Remove from heat and let cool slightly.
9. Preheat the oven to 375°F (190°C).
10. On a lightly floured surface, roll out the chilled dough to about ¼ inch thick.
11. Cut out circles of dough slightly larger than the tart pans.
12. Place the dough circles into the tart pans, pressing gently and trimming excess dough.
13. Spoon the raspberry filling into each shell, filling just to the top.
14. Brush the edges of the tart shells with the beaten egg for a golden finish.
15. Bake in the preheated oven for 20-25 minutes, until the crust is golden and the filling is bubbly.
16. Let the tarts cool in the pans for 10 minutes, then transfer to a wire rack. Dust with powdered sugar if desired before serving.

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