In a large bowl, whisk together the flour, powdered sugar, and salt. Add the cold, cubed butter and use a pastry blender or your fingers to cut the butter into the flour mixture until it resembles coarse crumbs.
In a separate small bowl, whisk the egg yolk with 2 tablespoons of ice water. Pour this mixture into the flour mixture. Mix until the dough just comes together. If needed, add the remaining tablespoon of ice water.
Form the dough into a disc, wrap it in plastic wrap, and chill in the refrigerator for at least 30 minutes.
On a lightly floured surface, roll out the chilled dough into a 12-inch circle. Carefully transfer the dough to a 9-inch tart pan with a removable bottom. Gently press the dough into the bottom and up the sides of the pan.
Trim any excess dough from the edges of the tart pan. Use a fork to prick the bottom of the crust several times.
Line the tart crust with parchment paper and fill it with pie weights or dried beans. Bake in a preheated oven at 375°F (190°C) for 15 minutes. Remove the parchment paper and pie weights and bake for another 5-7 minutes, or until the crust is lightly golden.
While the crust is baking, make the frangipane filling. In a large bowl, cream together the softened butter and granulated sugar until light and fluffy.
Add the ground almonds (almond flour) and almond extract to the butter mixture. Mix until well combined. Beat in the eggs one at a time, mixing well after each addition.
Spread the frangipane filling evenly over the pre-baked tart crust. Sprinkle the chopped pistachios over the frangipane.
Gently press the fresh raspberries into the frangipane filling.
Bake the Raspberry Pistachio Frangipane Tart in the preheated oven for 30-35 minutes, or until the frangipane is golden brown and set.
Let the tart cool completely in the pan before removing it.