In a medium bowl, combine flour, baking powder, salt, cinnamon and nutmeg; set aside. In the bowl of a stand mixer fitted with the paddle attachment, combine the butter and shortening and mix until combined. Add the sugar and brown sugar and beat until combined and creamy. Beat in the egg and vanilla. Mix in the pumpkin puree. Gradually add the dry ingredients and mix until just combined, scraping down the bowl as you go. Cover bowl tightly with plastic wrap and refrigerate for several hours or overnight. Dough should be firm enough to roll into balls.
After dough has been chilled, preheat oven to 350 degrees. Scoop about 2 Tablespoons of dough per cookie and roll into balls. Place on a lightly greased baking sheet, spacing two inches apart. Bake for about 12 minutes. Cookie will be puffed and lightly golden on the bottom. Remove from oven and using a 1/2 Tablespoon measuring spoon, press down in the center of the cookie, making an indentation. Cool on cookie sheet for 5 minutes, then remove to a wire rack and cool completely. When cookies are cool, fill indentation with cream cheese filling and drizzle with melted chocolate. Allow chocolate to set. Serve. Store leftover cookies in the refrigerator. Makes about 42 cookies.
Cream Cheese Filling: In a medium bowl, combine cream cheese and butter and mix until creamy. Add the powdered sugar, vanilla and salt and mix until well combined.
For Garnish: Place chocolate chips in a small bowl and the white chocolate chips in a separate small bowl. Add 1/2 teaspoon of shortening to each bowl. Microwave until chocolate is melted, stirring every 30 seconds until completely smooth. Using a fork, drizzle over cookies.