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Prepare the tart dough: In a large bowl, whisk together the all-purpose flour, granulated sugar, and salt. Add the cold, cubed unsalted butter and cut it into the flour mixture using a pastry blender or your fingertips until the mixture resembles coarse crumbs with some pea-sized pieces of butter remaining. 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. If needed, add up to 1 more tablespoon of ice water, 1 teaspoon at a time, until the dough comes together. Do not overmix. Form the dough into a disc, wrap tightly in plastic wrap, and refrigerate for at least 30 minutes.
Preheat the oven to 375°F. 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. Prick the bottom of the dough several times with a fork. Line the crust with parchment paper and fill with pie weights or dried beans. Bake for 15 minutes.
Remove the parchment paper and pie weights. Continue to bake the crust for another 5-7 minutes, or until lightly golden. Remove from the oven and set aside to cool slightly.
While the crust cools, prepare the frangipane: In a medium bowl, cream together the softened unsalted butter and granulated sugar until light and fluffy. Beat in the large eggs one at a time, mixing well after each addition. Stir in the almond flour, all-purpose flour, and almond extract until just combined.
Prepare the pears: In a separate bowl, toss the peeled, cored, and thinly sliced pears with the lemon juice, ground cinnamon, and ground nutmeg until evenly coated.
Assemble the tart: Spread the almond frangipane evenly over the bottom of the partially baked tart crust. Arrange the spiced pear slices decoratively on top of the frangipane, overlapping them slightly.
Bake the tart: Place the tart back into the 375°F oven and bake for 35-45 minutes, or until the frangipane is puffed, golden brown, and set in the center. A wooden skewer inserted into the frangipane should come out clean.
Prepare the glaze: While the tart is still warm, combine the apricot preserves and water in a small saucepan. Heat over low heat, stirring constantly, until the preserves are melted and smooth. Strain the mixture through a fine-mesh sieve if desired, to remove any fruit chunks.
Finish and serve: As soon as the tart comes out of the oven, brush the warm apricot glaze generously over the top of the pears and frangipane. Let the tart cool completely on a wire rack before slicing and serving. This allows the frangipane to fully set.

Prepare the tart dough: In a large bowl, whisk together the all-purpose flour, granulated sugar, and salt. Add the cold, cubed unsalted butter and cut it into the flour mixture using a pastry blender or your fingertips until the mixture resembles coarse crumbs with some pea-sized pieces of butter remaining. 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. If needed, add up to 1 more tablespoon of ice water, 1 teaspoon at a time, until the dough comes together. Do not overmix. Form the dough into a disc, wrap tightly in plastic wrap, and refrigerate for at least 30 minutes.
Preheat the oven to 375°F. 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. Prick the bottom of the dough several times with a fork. Line the crust with parchment paper and fill with pie weights or dried beans. Bake for 15 minutes.
Remove the parchment paper and pie weights. Continue to bake the crust for another 5-7 minutes, or until lightly golden. Remove from the oven and set aside to cool slightly.
While the crust cools, prepare the frangipane: In a medium bowl, cream together the softened unsalted butter and granulated sugar until light and fluffy. Beat in the large eggs one at a time, mixing well after each addition. Stir in the almond flour, all-purpose flour, and almond extract until just combined.
Prepare the pears: In a separate bowl, toss the peeled, cored, and thinly sliced pears with the lemon juice, ground cinnamon, and ground nutmeg until evenly coated.
Assemble the tart: Spread the almond frangipane evenly over the bottom of the partially baked tart crust. Arrange the spiced pear slices decoratively on top of the frangipane, overlapping them slightly.
Bake the tart: Place the tart back into the 375°F oven and bake for 35-45 minutes, or until the frangipane is puffed, golden brown, and set in the center. A wooden skewer inserted into the frangipane should come out clean.
Prepare the glaze: While the tart is still warm, combine the apricot preserves and water in a small saucepan. Heat over low heat, stirring constantly, until the preserves are melted and smooth. Strain the mixture through a fine-mesh sieve if desired, to remove any fruit chunks.
Finish and serve: As soon as the tart comes out of the oven, brush the warm apricot glaze generously over the top of the pears and frangipane. Let the tart cool completely on a wire rack before slicing and serving. This allows the frangipane to fully set.