Preheat oven to 350°F (175°C).
In a mixing bowl, whisk together flour, baking soda, cinnamon, nutmeg, and salt.
In another bowl, cream together the sugar and butter until light and fluffy.
Mix in the persimmon pulp, egg, and vanilla extract until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the chopped nuts if using.
Drop spoonfuls of dough onto a baking sheet.
Bake for 12-15 minutes or until edges are golden brown.
Let cookies cool on a wire rack.