Preheat oven to 350 degrees F. Line two rimmed baking sheets with silicone baking mats or parchment paper.
Cream the butter and sugar together (do this in the bowl of a stand mixer, in a regular mixing bowl with a hand mixer, or with a wooden spoon and elbow grease).
Once they're incorporated, add persimmon puree, eggs, and orange zest. Stir until combined.
In a small bowl, whisk the oat flour, rolled oats, baking soda, cinnamon, salt, and nutmeg together. Add to wet ingredients and mix until incorporated.
Stir in the nuts.
Scoop dough onto prepared baking sheets.
Bake for 12-15 minutes, until the oatcakes are browned. Rotate sheets halfway through baking, so that they cook evenly.
When time is up, remove oatcakes to a rack and let them cool.
Store oatcakes in an airtight container and keep in the refrigerator for up to 5 days. They can also be frozen for longer storage.