Combine buttermilk and baking soda together in a bowl.
Combine flour, baking powder, cinnamon, and salt in a separate bowl.
Mix persimmon pulp and sugar together in a large bowl. Beat in eggs. Add buttermilk mixture alternately with flour mixture, stirring until combined. Stir in heavy cream and melted butter. Pour batter into a 9×13-inch baking pan.
Bake in the preheated oven until edges pull away from the sides of the pan and cracks begin to appear in the center, 25 to 30 minutes. Chill until serving.