Step 1: Prepare the Pâte Sucrée (Sweet Pastry Crust): In a large bowl, whisk together the all-purpose flour, 1/4 cup granulated sugar, and salt. Add the cold unsalted butter, cut into small cubes. Using your fingertips or a pastry blender, cut the butter into the flour mixture until it resembles coarse crumbs with some pea-sized pieces remaining.
Step 2: In a small bowl, whisk the egg yolk with 2 tablespoons of ice water. Gradually add the egg mixture to the flour mixture, mixing until just combined and a dough forms. Be careful not to overmix, as this can develop the gluten and make the crust tough.
Step 3: Gather the dough into a disc, wrap it tightly in plastic wrap, and refrigerate for at least 30 minutes, or up to 2 days.
Step 4: 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. Prick the bottom of the crust all over with a fork.
Step 5: Line the crust with parchment paper and fill with pie weights or dried beans. Blind bake in a preheated oven at 375°F (190°C) for 15 minutes. Remove the weights and parchment, then continue to bake for another 5-7 minutes, until lightly golden. Let cool slightly.
Step 6: Prepare the Almond Frangipane Filling: In a medium bowl, cream together the softened 1/2 cup unsalted butter and 1/2 cup granulated sugar until light and fluffy. Add the almond flour, egg, vanilla extract, and almond extract. Mix until well combined and smooth.
Step 7: Spread the frangipane evenly over the blind-baked tart crust.
Step 8: Assemble and Bake the Pear and Almond Tart: Peel, core, and slice the fresh pears. Arrange the pear slices decoratively over the almond frangipane, pressing them gently into the filling. You can create a fan pattern or concentric circles for a beautiful presentation.
Step 9: Bake the Pear and Almond Tart in the preheated oven at 375°F (190°C) for 45-55 minutes, or until the frangipane is golden brown, set, and a skewer inserted into the center comes out clean. If the edges of the crust start to brown too quickly, you can loosely cover them with aluminum foil.
Step 10: Once baked, remove the Pear and Almond Tart from the oven and let it cool completely on a wire rack before slicing and serving. A dusting of powdered sugar can be added before serving.