In a large bowl, mix together the flour, powdered sugar, and salt. Add the cold, cubed butter. Using your fingers or a pastry blender, cut the butter into the flour mixture until it looks like coarse crumbs. Slowly add ice water, one tablespoon at a time, mixing gently after each addition, until the dough just comes together. Form the dough into a disk, wrap it in plastic wrap, and refrigerate for at least 30 minutes.
In a separate bowl, cream together the softened butter and granulated sugar until light and fluffy. Add the almond flour and salt, and mix until combined. Beat in the eggs one at a time, making sure each egg is fully incorporated before adding the next. Finally, stir in the almond extract.
Once the dough has chilled, take it out of the refrigerator. Lightly flour your work surface and rolling pin. Roll out the dough into a circle about 12 inches in diameter and about 1/8 inch thick. Gently 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.
Preheat your oven to 375°F (190°C). Pour the frangipane filling into the prepared tart crust and spread it evenly. Arrange the halved or quartered strawberries on top of the frangipane in a decorative pattern. Bake for 35-40 minutes, or until the crust is golden brown and the frangipane is set and lightly golden on top.
Let the Strawberry Almond Frangipane Tart cool in the pan on a wire rack for at least 20 minutes before removing the sides of the tart pan. If desired, brush warm apricot glaze over the strawberries. Let the tart cool completely before serving.