Preheat the oven to 375°F (190°C).
In a food processor, combine the flour, softened butter, powdered sugar, egg yolk, and cold water. Blend until the mixture resembles coarse crumbs.
Gather the dough into a ball, wrap it in plastic wrap, and refrigerate for 30 minutes.
Roll out the chilled dough on a floured surface to fit the tart pan. Carefully transfer the dough to the pan, pressing it into the bottom and sides. Trim any excess dough hanging over the edges.
Line the tart shell with parchment paper and fill it with baking beans or weights. Bake for 15 minutes, then remove the weights and parchment and bake for an additional 10 minutes until golden. Let it cool slightly.
In a bowl, combine the quartered figs, honey, chopped pistachios, vanilla extract, and salt. Mix gently to coat the figs.
Pour the fig mixture into the cooled tart crust, spreading it evenly.
Brush the edges of the crust with the beaten egg to give it a nice glaze, then bake for an additional 15 minutes or until the figs are bubbly and golden.
Allow the tart to cool for at least 15 minutes before slicing. Serve warm or at room temperature.