Make the Sweet Shortcrust Pastry: In a large bowl, whisk together the flour and powdered sugar. Add the cold, cubed butter. Using your fingertips or a pastry blender, work the butter into the flour until the mixture resembles coarse crumbs. In a separate small bowl, whisk together the egg yolk and ice water. Add this mixture to the flour and butter, and mix until just combined. Gently flatten the dough into a disk, wrap it in plastic wrap, and refrigerate for at least 30 minutes.

Chill the Dough: Refrigerate dough for at least 30 minutes.

Roll Out the Dough: Roll out the dough into a 12-inch circle, about ⅛ inch thick. Carefully transfer the dough to a 9-inch tart pan with a removable bottom. Press the dough into the pan, making sure it fits snugly into the corners and up the sides. Trim off any excess dough. Prick the base of the tart shell all over with a fork.

Blind Bake the Tart Crust: Preheat oven to 375°F (190°C). Line the tart crust with parchment paper and fill it with pie weights or dried beans. Bake for 20 minutes. Remove the parchment paper and pie weights. Bake for another 10-15 minutes, or until the crust is lightly golden brown. Let the crust cool slightly.

Make the Almond Frangipane Filling: In a medium bowl, cream together the softened butter and granulated sugar until light and fluffy. Beat in the eggs one at a time, mixing well after each addition. Stir in the almond flour and almond extract. Mix until just combined and smooth.

Assemble and Bake the Tart: Pour the almond frangipane filling into the pre-baked tart crust, spreading it evenly. Gently arrange the fresh blackberries over the frangipane filling, pressing them in slightly. Bake for 30-35 minutes, or until the frangipane is golden brown and set.

Cool and Glaze (Optional): Let the Blackberry Almond Frangipane Tart cool completely. Warm apricot jam until melted. Brush the warm jam lightly over the blackberries for a glaze.