Preheat the oven to 400 degrees F (200 degrees C) and place a rack in the center of the oven.
In the bowl of a food processor, pulse the All-Purpose Flour (2 1/2 cup), Granulated Sugar (2 teaspoon), Salt (1/2 tablespoon) together. Cut Unsalted Butter (1 cup) into small pieces, then add to the food processor. Pulse at one-second intervals until butter is the size of peas.
Add Water (1/2 cup) plus the extra tsp, and pulse again about ten times until the mixture is crumbly but holds together when pinched.
Lay two clean tea towels on a work surface. Dump half of the crumbly dough mixture into the center of each.
Grab the four corners of the towel together and twist to create a beggar's purse, pressing the dough into a disk. Use your hands to pack and pat the disk together. Store one of the rounds in the freezer for a future use. Keep one handy.
Combine Almond Flour (1/2 cup), Granulated Sugar (2 tablespoon), Salt (1 pinch), Butter (2 tablespoon) Egg (1) in the unwashed bowl of the food processor. Pulse until combined, then add Vanilla Extract (2 teaspoon). Purée until smooth.
On a lightly floured work surface, roll out the dough into a 12 or 13-inch round. Use as much flour as needed to prevent the dough from sticking, and every few rolls, flip the dough over.
Transfer dough to a parchment or Silpat-lined sheet pan. Spoon the frangipane into the center, leaving a 1-inch border.
Arrange the Apple (2) slices in concentric circles starting at the outer edge of the frangipane. Fold the exposed edge of dough towards the center to make a rustic enclosure.
Brush the edge of the dough with Butter (2 tablespoon) and flour. Drizzle the remainder over the exposed apples. Sprinkle the Natural Cane Sugar (2 tablespoon) over the top.
Bake for 35 minutes or until golden.
Remove pan from the oven and let rest on cooling rack for five to ten minutes or until Silpat or paper is cool enough to handle. Grab the edges of the paper or Silpat and slide to a cooling rack to cool further or to a cutting board to serve.
Cut into wedges. Serve on its own or with Vanilla Ice Cream (to taste).