In a large bowl, whisk together the flour and salt. Cut in the cold butter using a pastry blender or your fingertips until the mixture resembles coarse crumbs. Gradually add the ice water, one tablespoon at a time, mixing until the dough just comes together. Form the dough into a disk, wrap it in plastic wrap, and refrigerate for at least 30 minutes.

Lightly flour a clean surface. Roll out the chilled dough to a 12-inch circle. Carefully transfer the dough to a 9-inch tart pan with a removable bottom. Gently press the dough into the pan, trimming any excess. Prick the bottom of the crust with a fork.

Line the tart crust with parchment paper and fill with pie weights or dried beans. Bake in a preheated oven at 375°F (190°C) for 15 minutes. Remove the parchment paper and weights, and bake for another 5-7 minutes, or until the crust is lightly golden. Let cool slightly.

In a large bowl, cream together the softened butter and sugar until light and fluffy. Beat in the almond extract and vanilla extract. Add the eggs one at a time, beating well after each addition. Gradually add the almond flour, mixing until just combined.

Spread the frangipane filling evenly over the pre-baked tart crust. Arrange the pear slices in a decorative pattern on top of the frangipane. Sprinkle with sliced almonds, if desired.

Bake in the preheated oven for 35-40 minutes, or until the frangipane is golden brown and the pears are tender. If the crust starts to brown too quickly, you can loosely cover it with foil.

While the tart is baking, prepare the apricot glaze. In a small saucepan, heat the apricot jam and water over low heat until melted and smooth. Once the tart is out of the oven, brush the warm glaze over the pears for a glossy finish.

Let the Pear Frangipane Tart cool completely in the tart pan before removing it. Slice and serve.