Preheat the oven to 375°F (190°C).

In a mixing bowl, combine flour, sugar, and salt for the crust. Cut in the cold butter using a pastry cutter or your fingers until the mixture resembles coarse sand.

Add in the egg yolk and ice water and mix until the dough comes together. If the dough is too dry, add more water, 1 teaspoon at a time.

On a lightly floured surface, roll out the dough to fit a 9-inch tart pan. Gently press the dough into the pan, trimming any excess dough. Prick the bottom of the dough with a fork and place parchment paper over the dough. Fill the tart with baking beans or pie weights.

Bake the crust for 15 minutes, then remove the parchment paper and weights. Bake for an additional 10 minutes, until the crust is lightly golden brown. Let cool while you prepare the frangipane.

In a stand mixer or with a hand mixer, cream together the butter and sugar for the frangipane until light and fluffy. Add in the egg, almond flour, almond extract, and salt and mix until well combined.

Spread the frangipane evenly over the cooled crust.

Arrange the pear slices on top of the frangipane in a circular pattern, overlapping slightly.

In a saucepan, heat the apricot preserves and water over medium heat until melted and smooth. Using a pastry brush, brush the preserves mixture over the pears.

Bake the tart for 20-25 minutes, until the frangipane is set and the pears are tender.

Let the tart cool on a wire rack before serving. Serve warm or at room temperature.