The day before, place the palm shortening and ice-cold water in the refrigerator to chill overnight.
The following day, whisk together cassava flour, tigernut flour, arrowroot flour, coconut or date sugar, and sea salt in a large mixing bowl.
Remove the cold palm shortening from the fridge, cut into small pieces, then incorporate into the flour mixture using a pastry cutter or knife until pea-sized pieces are coated.
Add the chilled water and gently stir the mixture with a spatula until a rough, chunky dough forms. Avoid over-mixing.
Divide the dough into three equal portions, shape each into a ball, and refrigerate while prepping the persimmons.
Trim stems from the Fuyu persimmons, slice in half, then cut into ¼-inch thick slices with a serrated knife.
Preheat your oven to 400°F and line a baking sheet with parchment paper.
Prepare a work surface with parchment paper dusted lightly with arrowroot flour. Place one dough ball in the center and sprinkle with arrowroot flour.
Cover with another piece of parchment paper and press slightly by hand, then roll out carefully to about ⅛-inch thickness.
Spread 2 tablespoons of applesauce in the center of the dough disc, leaving about ¾-inch border around the edges.
Arrange the persimmon slices over the applesauce, then fold the edges of the dough inward around the fruit, pressing the folds to seal.
Transfer the galette to the lined baking sheet using a large spatula.
Repeat rolling and assembling with the remaining dough balls and persimmon slices.
Bake the galettes for 35 to 40 minutes, rotating the baking sheet halfway through, until golden brown.
Remove from the oven and enjoy the galettes warm right away.
