Preheat the oven to 350 degrees, and line a 12 cup muffin pan with cupcake liners.
In a large mixing bowl, with the paddle attachment, cream together the butter and sugar. Add the eggs, one at a time, beating between each addition. Then, add the persimmon.
Sift together the flour, baking powder, baking soda, salt, and pumpkin spice, and stir them very gently into the batter. Do not overmix. Add the sour cream and vanilla, until just combined.
Divide the batter between the 12 muffin cups.
Bake twenty minutes or until a toothpick comes out clean. Cool in the pan for five minutes, and then on a wire rack for ten minutes.
For the Vanilla Icing: Stir together the confectioner's sugar with four teaspoons of butter and one teaspoon of vanilla. Stir in the four teaspoons of water, one teaspoon at a time, until the icing is a good drizzling consistency.
Drizzle the icing on with a piping bag or a spoon.