A semi-free-form tart filled with honey-almond frangipane and a rainbow of apple slices topped with cardamom sugar.
Preheat the oven to 400 F.
In a small bowl, mix together 1 tablespoon of sugar and the ground cardamom.
On a large, lightly floured piece of baking parchment, roll out your pie dough into an 11-inch square. Use the parchment to transfer the dough to a 9-inch square tart pan, carefully removing the parchment and gently easing the dough into the tin. The dough should extend about a 1/2 inch over the edge of the tin. Place the tin in the refrigerator or freezer so that it will stay chilled while you prepare the filling.
In a medium bowl, use electric beaters to cream together the butter, pinch of salt, 25 g sugar, and honey until light and fluffy. Use the electric beaters to mix in a bit of the almond flour, then a bit of the egg, alternating between almond flour and egg until both are fully incorporated.
Halve and core the apples, and cut the apple halves into thin slices. (You can slice the apples lengthwise or crosswise--you're going for slices that will be between 2.5 and 2.75 inches in length.)
Remove the tart pan from the refrigerator, and scrape in the honey frangipane filling, using a spatula to smooth the frangipane into an even later. Top with the apple slices, arranging the slices in tightly packed rows. For an ombré effect, start with the apples with the darkest skin, and end with the lightest colored apples, as shown here:
Fold the the dough over the apples, the brush the dough with the lightly beaten egg.
Sprinkle the cardamom-sugar mixture over the apples (and over the crust, too, if you want!).
If you have time, place the pan in the freezer for 5 minutes. If not, you can just place it straight in the oven.
Bake the tart at 400 F for 50-60 minutes, until the frangipane is puffed and brown and the crust is golden.
Allow the tart, still in the pan, to fully cool on a wire rack. Once cool, remove the tart from the tin and serve.