Combine flours, sugar, and salt for the crust. Add to a stand mixer bowl or.a food processor and process with cubed butter. Add a few tbsp of cold water at a time to get the dough together.
The dough should not be sticky and it should be easy to form a ball. Wrap in plastic wrap and refrigerate for 30 minutes or longer.
Preheat oven to 400 F.
Slice persimmons and combine with all filling ingredients.
Take crust out of the fridge, roll it out on a floured surface, and add the filling, leaving ~ 1 inch of empty space at the perimeter. Fold the crust inward. (Optional: wash crust with nondairy milk - I didn't and my crust ended up super crisp.)
Bake for 35 min at 400 F (until crust is golden brown). Top with almonds, more thyme, and frozen coconut yogurt (as pictured) or your favorite ice cream!