These cookies are a favorite in the fall when ripe persimmons are abundant. Hachiya persimmons work best, but make sure they're extremely ripe before using, otherwise the fruit is unpleasantly astringent. An equal amount of pumpkin purée can be substituted for the persimmon if you prefer.
Position a rack in the center of the oven and preheat to 350 degrees F.
Purée the persimmons in a food processor or blender. Set aside 1 cup of purée and freeze the rest for another use.
In a large bowl cream the butter and sugar until smooth. Beat in the egg, then add the persimmon purée.
In another bowl, whisk together the flour, baking powder, baking soda, salt and spices. Add the dry mixture to the persimmon batter, stirring to blend. Stir in the raisins and walnuts, if using.
Drop teaspoonfuls of cookie batter onto ungreased cookie sheets, pressing the dough slightly to flatten. Bake until the cookies are set and slightly browned, 10 to 12 minutes. Let cool on a wire rack.
Meanwhile, make the glaze by whisking together the confectioner's sugar, orange juice and allspice. Let the cookies cool for 15 minutes before glazing.