Puree the persimmons in a mini food processor or blender until smooth; set aside.
Whisk the flour, baking soda, cinnamon, cloves, nutmeg and salt in a medium bowl. Beat the butter and granulated sugar in a large bowl with a mixer on medium-high speed until light and fluffy, about 2 minutes. Beat in the egg and vanilla until combined, then beat in 3/4 cup of the persimmon puree until combined. (The mixture may look curdled.) Reduce the mixer speed to low; gradually add the flour mixture, beating until just incorporated. Fold in the raisins with a rubber spatula. Cover and refrigerate until firm, about 30 minutes.
Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Line 2 baking sheets with parchment paper. Scoop heaping tablespoonfuls of dough about 2 inches apart on the prepared baking sheets. Bake, switching the pans halfway through, until the cookies are golden brown, about 13 minutes. Let cool completely on the baking sheets.
Make the glaze: Whisk the confectioners' sugar and milk in a small bowl. Spoon about 1 teaspoon of the glaze over each cookie, then sprinkle with the pistachios. Let set, 10 minutes.