For the crust: Make the dough: In a food processor, pulse the flour, sugar, and salt until combined. Add the cold, cubed butter and pulse until the mixture resembles coarse crumbs. Add the egg yolk and pulse again until just combined. Gradually add cold water, one tablespoon at a time, until the dough starts to come together.

1. Chill the dough: Turn the dough out onto a floured surface, shape it into a disc, wrap it in plastic wrap, and refrigerate for at least 30 minutes.
2. Preheat the oven: Preheat your oven to 350°F (175°C). On a floured surface, roll out the dough to fit a 9-inch tart pan. Press the dough into the bottom and up the sides of the pan. Trim any excess dough.
3. Bake the crust: Place a piece of parchment paper over the dough and fill it with pie weights or dried beans. Bake for 15 minutes, then remove the weights and parchment paper. Bake for an additional 10-12 minutes, or until the crust is golden brown. Let it cool completely before filling.
4. For the filling: Prepare the chocolate mixture: In a heatproof bowl, combine the chopped chocolate, heavy cream, and milk. Place the bowl over a pot of simmering water (double boiler method), stirring until the chocolate is completely melted and smooth. Remove from heat.
5. Add butter and vanilla: Stir in the butter and vanilla extract until the mixture is fully combined and glossy.
6. Assemble the tart: Pour the chocolate filling into the cooled tart crust, smoothing it out with a spatula. Sprinkle the chopped toasted hazelnuts over the top.
7. Chill the tart: Refrigerate the tart for at least 2 hours, or until the filling is set and firm.
8. Serve: Once chilled, slice the tart and serve. Enjoy the indulgent, chocolate-hazelnut goodness!