Preheat the oven to 325 degrees F. In a 4-cup measuring cup, measure out the persimmon pulp; give it a good mash with a fork until it’s resembles a smooth(ish) puree. Stir in the baking soda, white granulated sugar, brown sugar, melted butter, egg and vanilla extract
In a medium bowl, whisk together the all-purpose flour, baking powder, cinnamon and salt. Pour the wet ingredients into the dry ingredients and mix until combined, being sure not to over mix the batter. Transfer to a 7-inch round baking dish (alternatively you could use a 8x5 or 9x5-inch loaf pan). Bake in the oven for 45 to 50 minutes, until the center puffs up slightly and the edges pull away from the pan.
While the pudding is baking, make the toffee sauce. In a small bowl, mix together the vanilla bean caviar and brown sugar together. In a medium saucepan, set over medium low heat, add the vanilla brown sugar and butter. Cook until the butter has melted and the brown sugar begins to caramelize, about 2 to 3 minutes. When the brown sugar begins to bubble, add the heavy cream and stir. Cook for an additional 3 minutes. During this time the toffee sauce will thicken and reduce by a little bit.
When the persimmon pudding comes out of the oven, pour the warm toffee sauce over the pudding and sprinkle with a few generous pinches of sea salt.