In a medium bowl, add cream cheese and powdered sugar. Use a hand mixer to blend until smooth and creamy. Add in vanilla and ground cinnamon for filling, beating until just combined.
Form the cream cheese filling into 1 tsp balls (you should end up with at least 15) and place on a parchment paper lined plate. Freeze until solid, about 1 to 2 hours.
In a medium bowl, whisk together flour, baking soda, salt, cinnamon, pumpkin pie spice, and nutmeg until combined. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat together butter and sugars until light and fluffy, about 2 minutes. Add pumpkin and vanilla, mixing until just combined. It will look a little curdled and this is ok.
Add in dry ingredients and beat until just combined. Make sure not to over mix. Gently fold in graham cracker pieces.
Scoop out 1/3 cup of the dough and form it into a ball. Place on a lined baking sheet. Repeat with the rest of the dough to get at least 15 cookies. Chill in the refrigerator for at least 1 to 2 hours.
When ready to bake, preheat oven to 325˚F. Line two baking sheets with parchment paper or silicone mats. You can use the ones you used to chill the dough!
Remove dough from the fridge. Take one ball and use your knuckle to form a deep indent in the center. Place a frozen cheesecake ball in the indent. Cover up the cheesecake ball with the dough, making sure it is completely covered. Place seam side down on baking sheets.
Bake for 20 to 25 minutes, until the cookies are set and no longer wet-looking. Remove cookies and let them cool on the baking sheets for at least 10 minutes before cooling completely on a wire cooling rack.
Store in the refrigerator once cooled, in an airtight container, for up to 1 week. They will also last for 3 days at room temperature.