Preheat your oven to 300 degrees F. Grease a 9” by 13” pan and set aside.
Combine melted butter, brown sugar, vanilla, ginger, milk, and eggs in a mixing bowl. Mix thoroughly.
Combine flour, baking soda, baking powder, and cinnamon in a separate bowl.
Add ⅓ of your dry ingredients to your wet ingredient mixture and stir. Then add ⅓ of your persimmon pulp to aforementioned mixture and stir. Repeat this process until all three are combined. The batter will be very runny.
Transfer the batter to a 9" x 13" greased baking dish and bake for 30 minutes.
While the pudding is baking, make your caramel caramel sauce. Combine sugar, milk, and butter over medium heat. Bring to a boil, cook until thickened (1-2 minutes) before removing from heat. Stir in vanilla extract.
Serve persimmon pudding warm, drizzled with caramel sauce. It will have a cake-like crust and a custard-like center.