Step 1: Prepare the Linzer Pastry Crust: In a large bowl, whisk together all-purpose flour, almond flour, granulated sugar, and salt. Cut in the cold cubed butter using a pastry blender or your fingertips until the mixture resembles coarse crumbs with some pea-sized pieces of butter remaining.
Step 2: In a small bowl, whisk the egg yolk and vanilla extract. Add this to the flour mixture, along with 2 tablespoons of ice water. Mix until the dough just comes together, adding the remaining tablespoon of ice water if needed, one teaspoon at a time. Do not overmix.
Step 3: Divide the dough in half. Form each half into a disk, wrap tightly in plastic wrap, and refrigerate for at least 1 hour (or up to 2 days).
Step 4: Once chilled, on a lightly floured surface, roll out one disk of dough into a 12-inch circle. Carefully transfer it to a 9-inch tart pan with a removable bottom. Press the dough gently into the bottom and up the sides. Trim any excess dough. Prick the bottom of the crust all over with a fork. Place the tart shell in the freezer for 15 minutes.
Step 5: Preheat oven to 375°F (190°C). Remove the tart shell from the freezer, line it with parchment paper, and fill with pie weights or dried beans. Blind bake for 15 minutes. Remove the parchment and weights, and bake for another 5-7 minutes, or until the crust is lightly golden. Let cool slightly.
Step 6: Prepare the Pistachio Cream: In a food processor, combine the lightly toasted pistachios and granulated sugar. Process until the pistachios are finely ground. Add the softened butter and process until smooth.
Step 7: Add the eggs, vanilla extract, almond extract (if using), flour, and salt to the pistachio mixture. Process until well combined and creamy, scraping down the sides as needed.
Step 8: Prepare the Pears: Peel, core, and halve the pears. Slice them thinly (about 1/8-inch thick). Toss the pear slices gently with lemon juice and 1 tablespoon of granulated sugar to prevent browning and add a touch of sweetness.
Step 9: Assemble the Tart: Pour the pistachio cream into the pre-baked tart shell and spread evenly. Arrange the sliced pears decoratively on top of the pistachio cream, starting from the outside edge and working your way in, slightly overlapping each slice.
Step 10: Using the second disk of dough, you can either create decorative cut-outs (like leaves or strips) to place on top of the pears, or simply roll it out and cut into strips to create a lattice pattern over the pears. Alternatively, you can omit this step for a simpler look.
Step 11: Bake the tart at 375°F (190°C) for 45-55 minutes, or until the crust is golden brown and the pistachio cream is set and lightly puffed. If the crust edges brown too quickly, loosely cover them with foil.
Step 12: Let the tart cool completely on a wire rack before removing it from the pan. Dust with powdered sugar just before serving. Serve at room temperature.