Preheat the oven to 350.
Add butter, sugar, and brown sugar to a stand mixer or large bowl. Mix for 2 minutes until smooth. Add pumpkin puree, eggs, and vanilla. Mix until just combined.
Add flour, pumpkin pie spice, baking soda, baking powder, and salt. Mix until just combined.
To make the streusel, add brown sugar, butter, cinnamon, and salt to a small bowl. Stir with a spoon until well combined.
Using a large cookie scoop (at least 1/4 cup), scoop the dough onto a lined or greased baking sheet. Using your fingers, flatten each dough ball slightly. The dough will be slightly sticky, so wetting your fingers first works best.
Scoop a small dollop (about 1/2 tsp) of cinnamon streusel onto each cookie. Using your finger, spread the streusel evenly across the top of each cookie.
Bake the cookies for 11-13 minutes, until they are just set.
While the cookies cool slightly, make the frosting. Combine butter and cream cheese and mix for 2 minutes. Add powdered sugar and vanilla and mix again until smooth. Transfer frosting to a piping bag and pipe a swirl of frosting onto each cookie. Enjoy!