Preheat oven to 375 degrees Fahrenheit. Position baking rack in center of oven.
To prep the crust, begin by weighing out flours, sugar, salt, butter, and shortening in a medium mixing bowl. Using your hands, work the butter and shortening into the dry ingredients, allowing clumps to begin to form. You should have a loose texture of clumpy sand.
In a separate small bowl, stir together the apple cider vinegar, vanilla bean paste, and ice water. Using a tablespoon measuring spoon, spoon in the water mixture. Using your hands, mix the dough together until it forms a loose ball. Using both hands, form the dough into a round disc. Loosely cover with a clean kitchen towel or plastic wrap and chill in the fridge for about 10 minutes.
Roll out dough on a floured work surface and place into your 10-inch tart pan. Use your fingers to shape the tart shell in the pan, pressing the sides into the fluted mold. Use a fork to lightly prick the surface. Line the tart shell with foil and add your pie weights to cover the top. Bake for 15 minutes then remove to cool slightly before removing pie weights. Lower oven heat to 350 degrees Fahrenheit.
While the tart shell cools, whisk together the persimmon butter and remaining custard ingredients. Pour custard into the slightly cooled tart shell.
Bake for 1 hour, checking the tart at the 50 minute mark to ensure the center isn’t too wiggly or wet. Depending on oven settings, you may need about 10 minutes more. Remove from oven once center is set. Cool completely and allow to set for 4 hours before garnishing with whipped créme fraîche and a dusting of ground cinnamon.
For the whipped créme fraîche, use a hand mixer to whip together the créme fraîche, heavy cream, and maple syrup. Whip on high speed until stiff peaks form. Portion into a piping bag fitted with your desired large tip design and pipe the whipped topping along the outer edge of the cooled tart.