Preheat oven to 350 degrees F (175 degrees C). Line a baking sheet with parchment paper or a Silpat(R) nonstick baking mat.
Mash persimmon pulp in a small bowl and stir in baking soda to let mixture congeal.
Beat white sugar and 1/2 cup butter with an electric mixer in a large bowl until light and fluffy. Stir flour, cinnamon, cloves, nutmeg, and salt together in a second bowl.
Mix egg into the persimmon mixture. Add persimmon mixture and flour mixture to the creamed butter mixture and stir well to combine. Fold pecans and raisins into the batter.
Drop batter onto the prepared baking sheet using a medium cookie scoop.
Bake in the preheated oven until slightly browned and puffy, 13 to 15 minutes. Remove from oven and cool completely on wire racks, about 30 minutes.
Mix confectioners' sugar, maple syrup, 1 tablespoon melted butter, vanilla extract, and salt in a bowl until maple glaze is smooth. Place a sheet of parchment paper under the wire rack to catch the drips. Drizzle maple glaze onto the cookie tops using a spoon. Let set until glaze hardens, about 30 minutes.
Cut green belt candy into small leaf shapes using kitchen scissors. Combine white chocolate and shortening in a microwave-safe glass or ceramic bowl and melt in the microwave in 15-second intervals, stirring after each melting, 1 to 3 minutes.
Drip some melted white chocolate over each cookie using a spoon. Place one red candy-coated chocolate piece in the middle of each cookie and add a green belt leaf to each side. Let set until frosting hardens, about 30 minutes.