Step 1: Prepare the pastry by pulsing flour, sugar, and cold butter in a food processor until it reaches a sandy texture.
Step 2: Add the egg yolk and ice water, pulsing until the dough just begins to clump together.
Step 3: Form the dough into a disk, wrap in plastic, and refrigerate for at least 30 minutes to rest the gluten.
Step 4: Pre-heat your oven to 375°F (190°C). Roll out the chilled dough and fit it into a 9-inch tart pan with a removable bottom.
Step 5: Line the dough with parchment paper and pie weights, then blind-bake for 15 minutes. Remove weights and bake for another 5 minutes.
Step 6: Make the frangipane by creaming the room temperature butter and sugar until light and fluffy.
Step 7: Beat in the egg, almond flour, vanilla extract, and almond extract until the mixture is smooth and aerated.
Step 8: Spread the frangipane evenly into the pre-baked tart shell using an offset spatula.
Step 9: Thinly slice the pear halves crosswise and arrange them in a starburst pattern on top of the frangipane.
Step 10: Bake the Pear and Almond Tart for 35-40 minutes until the filling is puffed and golden brown. Brush with warmed apricot jam while still hot.