Whirl the pulp in a blender until smooth. Blend together the persimmon pulp and bicarb soda in a small bowl.
In a large bowl, cream together the butter and sugar until fluffy. Add the puree to the creamed mixture. Sift together the flour, baking powder, salt, cinnamon, nutmeg and cloves; gradually blend the flour mixture into the persimmon mixture. Stir in nuts and zest. Batter will be stiff. Spoon into a greased and floured 20cm square cake pan.
Bake at 180 degrees C for 40 to 45 minutes, or until a toothpick inserted in the centre comes out clean. Cool the cake in the pan for 10 minutes and turn out on a rack to continue cooling an additional 20 or 30 minutes before serving. Sprinkle with icing sugar and serve warm.