Preheat oven to 300 degrees F (150 degrees C). Grease and flour a 9x13 inch cake pan.
Whisk together the flour baking powder, baking soda, salt, and sugar in a bowl, set aside. Whisk together the eggs, persimmon pulp, milk, and vanilla extract in a separate bowl until smooth. Fold the persimmon mixture into the flour mixture until no dry lumps remain. Pour into the prepared pan.
Bake in preheated oven until a toothpick inserted into the center comes out clean, about 1 hour 15 minutes. Cool in the pan for 10 minutes, then remove from the pan, and allow to cool completely on a wire rack before icing.