For the crust:
1 egg yolk
2 tbsp. very cold water
1 tsp. vanilla extract
1 1/4 cups all-purpose flour
1/3 cup sugar
1/4 tsp. salt
8 tbsp. cold unsalted butter, cut into 1/4-inch cubes
For the filling:
5 oz. bittersweet chocolate, finely chopped
½ cup heavy cream
4 tbsp. unsalted butter, cut into 4 pieces
2½ tbsp. sugar
2 large eggs, at room temperature
1 large egg yolk, at room temperature
1 cup (6 oz.) fresh raspberries, rinsed and dried
To make the crust, in a small bowl stir together the egg yolk, water and vanilla; set aside. Combine the flour, sugar and salt in the bowl of a stand mixer fitted with the paddle attachment. Add the butter and beat on medium-low speed until the mixture resembles coarse cornmeal, with butter pieces no larger than small peas. Add the egg mixture and beat on low speed just until the dough comes together. Wrap in plastic wrap and refrigerate until well chilled, about 30 minutes.
Preheat the oven to 400˚ F. When you are ready to roll out the dough, unwrap it and place it on a lightly floured work surface. Roll out with a floured rolling pin, lifting and turning the dough occasionally to prevent it from sticking to the work surface. Roll it out evenly until it is large enough to line a 9-inch tart pan and is about 1/8-inch thick. Carefully transfer the dough to the tart pan, pressing it into the sides, and trim to remove the excess.
Cover the dough with foil or parchment paper and fill with baking beads. Bake for 20 minutes. Remove the foil and baking beads and using a fork, gently poke holes in the bottom and sides of the crust. Bake until the crust is golden, 5-10 minutes more. Transfer to a wire rack and let cool completely. Reduce the oven temperature to 300˚ F. Place the tart pan on a baking sheet.
Set a heatproof bowl over a pan of simmering water. Add the chocolate to the bowl and heat, stirring occasionally, until completely melted. Remove from the heat. Meanwhile, bring the cream and the butter just to a boil.
Pour the cream-butter mixture over the chocolate and let stand 30 seconds. Whisk together gently until smooth and well combined. Then stir in the sugar, eggs and egg yolk. Rap the bowl against the counter gently to break any bubbles that might have formed. Scatter the berries over the bottom of the crust, then pour the chocolate mixture over the berries. Bake for about 30 minutes, so that the filling does not jiggle if you tap the pan. Transfer the pan to a wire rack and let cool to room temperature before serving.