Prepare the persimmon filling: Preheat your oven to 350°F (175°C). Peel and remove the seeds from the persimmons. Mash the pulp to get about 1 ½ cups. In a large bowl, whisk together the persimmon pulp, flour, sugar, egg, baking powder, cinnamon, nutmeg, and salt until well combined. Pour this mixture into a greased 8x8-inch baking dish.
Make the oatmeal topping: In a separate bowl, combine the oats, brown sugar, flour, and a pinch of salt. Add the cold butter cubes and use your fingers or a pastry cutter to mix until the mixture resembles coarse crumbs.
Assemble the bars: Evenly sprinkle the oatmeal topping over the persimmon mixture. Make sure it covers the entire surface.
Bake: Place the baking dish in the preheated oven and bake for 35-40 minutes, or until the top is golden brown and the center is set. A toothpick inserted into the center should come out clean.
Cool and serve: Allow the bars to cool completely in the dish, about 1 hour. Cut into squares and serve.