Preheat the oven to 350°F. Line a baking sheet with parchment paper and set aside.

In a stand mixer fitted with the paddle attachment, beat the butter, brown sugar, and granulated sugar on low speed to combine, about 1 minute.

Scrape down the sides and bottom of the bowl, then add the egg and vanilla. Beat until combined.

Stop the mixer and scrape down the bowl, then add the flour, graham cracker crumbs, baking powder, and salt. Beat on low speed until just combined.

Use a 2-ounce cookie scoop to portion out equal amounts of dough, rolling them between your hands to smooth out the edges. Place on the prepared baking sheets, spacing the dough 2 inches apart. Press your thumb into the center of each dough ball to make a wide divot.

Place the cookies in the preheated oven and set a timer for 5 minutes.

While the cookies bake, make the pumpkin filling. In a small bowl, combine the pumpkin, brown sugar, egg, evaporated milk, flour, and pumpkin pie spice. Whisk to combine.

Remove the cookies from the oven after 5 minutes and reshape the divot in the middle of each cookie. Spoon about 2 teaspoons of the pumpkin filling into the center of each cookie.

Place the cookies back in the oven for 9 to 11 more minutes or until the cookies are turning a light golden brown and the filling is no longer wobbly.

Remove the baking sheet from the oven and allow the cookies to rest for 5 minutes, then transfer to a cooling rack to cool completely.

Once cool, top with a dollop of whipped cream if desired and serve.