Preheat your oven to 375°F (190°C). Carefully unroll the pie crust into a 9-inch tart pan with a removable bottom, pressing the dough gently into the base and up the fluted sides. Trim any excess dough from the edges.

In a medium mixing bowl, beat the softened butter and granulated sugar together using an electric mixer until light and fluffy, which should take about 2 minutes.

Add the egg, vanilla extract, and almond extract to the butter mixture. Beat on medium speed until the wet ingredients are well combined and smooth.

Gently fold the almond flour, all-purpose flour, and salt into the butter mixture until a thick, uniform paste forms. This creates your rich frangipan filling.

Using a rubber spatula, spread the frangipan filling in an even layer across the bottom of your prepared tart shell.

Arrange the thinly sliced apples in a tight, overlapping concentric circle over the frangipan filling, starting from the outside edge and working your way into the center.

Bake the tart on the middle rack of the preheated oven for 40 to 45 minutes, or until the frangipan is puffed and deeply golden brown, and the apples are fork-tender.

Remove the tart from the oven and immediately brush the warm apples with the warmed apricot jam to give the dessert a beautiful, glossy sheen.

Allow the tart to cool in the pan on a wire rack for at least 20 minutes before carefully removing the sides. Slice into wedges and serve warm with a dusting of powdered sugar or a scoop of vanilla bean ice cream.