The day before, chill the palm shortening and water in the fridge overnight to ensure they are very cold.
The next day, whisk together cassava flour, tigernut flour, arrowroot flour, coconut sugar (or date sugar), and sea salt in a large mixing bowl.
Remove the palm shortening from the fridge and chop into small pieces with a sharp knife.
Incorporate the cold palm shortening into the flour mixture using a pastry cutter or sharp knife until the fat pieces resemble peas and are well coated with flour.
Pour in the ice-cold water and gently stir with a rubber spatula until a rough, chunky dough forms; avoid overmixing.
Divide the dough into three equal parts, shape each into a ball, and refrigerate while preparing the persimmons.
Trim the stems from the Fuyu persimmons, cut them in half, then slice each half into ¼-inch thick pieces using a serrated knife.
Preheat oven to 400°F and position a rack in the center; line a baking sheet with parchment paper.
Lay a large piece of parchment on your work surface and lightly dust it with arrowroot powder.
Place one dough ball in the center of the parchment and sprinkle it with arrowroot powder; cover with another piece of parchment and gently press down.
Roll out the dough carefully into a disc about ⅛-inch thick.
Spoon 2 tablespoons of applesauce onto the center of the disc, leaving about ¾-inch clear at the edges.
Arrange persimmon slices over the applesauce layer.
Fold the edges of the dough up and over the filling, creating pleats and pressing to seal.
Transfer the assembled galette onto the prepared baking sheet using a large spatula; repeat with remaining dough balls.
Bake for 35 to 40 minutes, turning the baking sheet halfway through, until the crust is golden and crisp.
Serve the galettes warm, straight from the oven, for a cozy dessert or snack.
