Combine the flour, sugar, almond flour and salt in a large bowl. Add the butter cubes and, using a pastry cutter (or your fingers), cut the butter into the dry ingredients until the texture resembles sand, with butter pieces no larger than small peas. You can also use a food processor if that's easier.

Add the vanilla extract and egg, and, using your hands, work the dough just until it comes together and is smooth. Then, form a ball, flatten and wrap in plastic. Refrigerate for at least 2 hours before rolling.

When ready to roll, preheat the oven to 350F. Transfer the dough to a work surface lightly dusted with flour. Lightly dust the top of the dough and the rolling pin with flour, and roll out the dough into a circle at least 12 inches in diameter and about 1/8 inch thick.

Place in a buttered and floured pie plate. Trim the edges and crimp.

Cover the bottom of the pie with a large square of parchment paper or aluminum foil, snugging the lining right against the edges and sides of the pie. The, fill the pie with pie weights or beans, making sure they cover the bottom.

Bake the crust until the edges are barely golden, about 15 minutes. Then, remove the pie weights and return the crust to the oven, baking again until the bottom looks dry, another 5 minutes. Remove from the oven and let it cool down before filling.

Slice the apples, making sure they are not too thin or they will get too soft when cooking.

Transfer the apples to a bowl and toss with the sugar.

In a large skillet, over medium heat, melt the butter and cook the apples until golden, about 10 minutes. Remove from heat and reserve.

Using a hand mixer (or whisking by hand), whisk the butter until fluffy. Then, add the sugar and egg and mix until smooth.

Add the flour and corn starch and mix well, until there are no lumps left. Add the rum (or vanilla extract) last and give it a last good mix.

Spread the almond cream on the pie crust. Then, distribute the apple slices over the cream, without pressing down too much as the cream will grow around the apples.

Bake in the preheated oven for 30 minutes or until the filling is set.

Dust with confectioner's sugar and serve.