Preheat the oven to 300 degrees F (150 degrees C). Coat a 9x13-inch baking dish with cooking spray.

Whisk flour, white sugar, brown sugar, baking soda, baking powder, cinnamon, and salt together in a large bowl until thoroughly combined. Briefly beat eggs together in a separate large bowl, then whisk in milk until smooth.

Add flour mixture to egg mixture in batches, alternating with persimmon pulp, mixing well after each addition. Stir in melted butter; transfer to the prepared baking dish.

Bake in the preheated oven until a toothpick inserted into center comes out clean, about 1 hour. Cool before serving.