Preheat your oven to 350°F (175°C) and grease a baking dish.
In a large mixing bowl, combine persimmon pulp and sugar, mixing until well blended.
In another bowl, sift together flour, baking soda, baking powder, cinnamon, and nutmeg.
Stir the dry ingredients into the persimmon mixture alternately with the milk, beginning and ending with the flour mixture.
Add melted butter and beaten eggs into the mixture and mix until smooth.
Pour the batter into the prepared baking dish and bake for 1 hour, or until a toothpick inserted into the center comes out clean.
Let the pudding cool slightly before serving.