Preheat the oven to 350F and line a large baking sheet (or two) with parchment paper.
Add the softened butter and light brown sugar to the bowl of a stand mixer fitted with the paddle attachment. Beat on medium speed until light and fluffy– about 2 minutes.
Next, add the pumpkin puree, egg, and vanilla. Mix again until well combined. Scrape down the sides of the bowl as needed.
Next, add 1 ¼ cups of graham cracker crumbs, along with the flour, 1 teaspoon pumpkin pie spice, and baking soda. Mix just until the dry ingredients are fully incorporated– you don’t want to overmix!
Scoop out 2 tablespoon sized portions and roll them into smooth balls.
In a small bowl, stir together the remaining ½ cup graham cracker crumbs and ½ teaspoon pumpkin pie spice. Roll the cookie dough balls in the graham cracker crumbs and then place them on the parchment lined baking sheet (make sure to place them at least 2” apart). Press each dough ball into a ½” thick disc.
Bake for 10-12 minutes, or just until the edges of the cookies are set. For chewy cookies, make sure not to overbake!
Remove the cookies from the oven and allow them to cool completely on the baking sheet. When the cookies are cool, make the cheesecake frosting (below).
For the Cheesecake Frosting
Add the softened cream cheese, softened butter, and pumpkin pie mix to the bowl of a stand mixer fitted with the paddle attachment. Beat on medium speed until well combined– about 1 minute.
With the mixer on low speed, slowly add the powdered sugar, followed by the vanilla extract.
Turn the mixer to medium-high speed and whip until the frosting is light and fluffy– about 1 minute. Scrape down the sides of the bowl as needed.
Transfer the frosting to a piping bag fitted with your choice of tip (I’m using a Wilton 12).
When the cookies are cool, pipe the frosting over the cookies and sprinkle with any remaining graham cracker-pumpkin pie spice mixture. Enjoy immediately.
Store any leftovers in an airtight container in the fridge for up to three days.