Preheat the oven to 350°F. Line two sheet pans with parchment paper. Set aside.
To make Cookies: In a large bowl use a whisk to sift together graham cracker crumbs, flour, baking powder, baking soda and salt.
In a separate bowl, with an electric mixer on medium speed cream the butter until light and fluffy. About 2 minutes.
To the butter add granulated sugar, pumpkin puree, vanilla extract, cinnamon, ginger, nutmeg and clove (OR allspice). Mix on medium speed until fully combined. Add eggs one at a time beating well after each addition.
Gradually add the sifted dry ingredients to the creamed mixture mixing on low speed just until combined. Stop and scrape the sides of the bowl periodically.
To make Cheesecake Filling: In a separate medium size bowl, use an electric mixer to beat the cream cheese for 1-2 minutes. Add granulated sugar, pumpkin puree, vanilla extract, ground cinnamon and salt. Beat for 2 minutes or until fully combined and smooth.
Use a medium cookie scoop to divide the dough. Roll into balls placing them at least 2 inches apart on sheet pans. (14 cookies per baking sheet if you are using 2 large sheets or bake in batches)
Use a teaspoon to make a well in the center of each cookie ball. Fill the cookie with a heaping teaspoon of the cheesecake mixture. (You can also use a pastry tamper to create the center.)
Bake for 12-14 minutes or until golden and the filling is set when the pan is gently shaken. Allow the cookies to sit on the pan for 10 minutes then transfer to a cooling rack to cool completely.
Once the cookies have cooled down you can drizzle them with caramel sauce, if desired. Serve at room temperature or cold.