Make the crust: In a medium bowl, whisk together the flour, 2 tablespoons sugar, and salt. Add the cold butter cubes and use your fingertips to work the butter into the flour until the mixture looks like coarse crumbs with some pea-sized pieces remaining. Add ice water one tablespoon at a time, stirring with a fork after each addition, just until the dough holds together when you press a bit between your fingers. Do not over-mix.

Press the dough evenly into the bottom and up the sides of a 9-inch removable-bottom tart pan. The layer should be about 1/8-inch thick all the way around. Prick the bottom all over with a fork. Place the pan in the freezer for 15 minutes while you prepare the almond cream and apples. Preheat your oven to 375 degrees F.

Make the almond cream: Beat the softened butter and 1/2 cup sugar together with a hand mixer or stand mixer on medium speed until light and fluffy, about 2 minutes. Add the almond flour, eggs, vanilla extract, cardamom, and cinnamon. Beat on low speed until the mixture is smooth and creamy. It should look like a thick, pale paste.

Remove the tart pan from the freezer. Spread the almond cream evenly over the chilled crust using a small offset spatula or the back of a spoon. Go all the way to the edges.

Fan the apple slices over the almond cream in overlapping concentric circles, starting at the outer edge and working toward the center. Press them gently into the cream so they sit flat. The apples will shrink a little during baking, so layer them slightly more than you think you need.

Bake on the center rack for 35 to 40 minutes. The almond cream should be puffed, set, and golden brown around the edges and through the center. A toothpick inserted between the apple slices into the cream should come out clean. If the edges of the crust start to brown too fast after 25 minutes, cover them loosely with strips of foil.

While the tart bakes, warm the apricot jam and 1 teaspoon of water in a small saucepan over low heat, stirring until smooth and runny. Remove from heat. As soon as the tart comes out of the oven, brush the warm glaze over the apple slices and almond cream using a pastry brush. Let the tart cool in the pan on a wire rack for at least 20 minutes before removing the sides and slicing.