Preheat your oven to 350°F (175°C).
In a large bowl, cream together the softened butter, brown sugar, and granulated sugar.
Add in the pumpkin puree and egg, mixing well until smooth.
In a separate bowl, whisk together the flour, baking soda, cinnamon, and nutmeg.
Gradually mix the dry ingredients into the wet ingredients.
Fold in the chocolate chips and graham cracker crumbs.
Using a cookie scoop, drop dough onto a lined baking sheet, leaving space between each cookie.
Bake for 10-12 minutes, or until the edges are golden brown.
Allow cookies to cool on the baking sheet for 5 minutes before transferring to wire racks.