**Preheat the Oven:** Preheat your oven to 350°F (175°C) and line a cookie sheet with parchment paper or a silicone baking mat.
**Make the Cookie Dough:** In a large mixing bowl, cream together the butter, brown sugar, and granulated sugar until light and fluffy, about 3-4 minutes. Add the egg, vanilla extract, and pumpkin puree, and mix until smooth.
**Combine Dry Ingredients:** In a separate bowl, whisk together the oats, flour, baking soda, baking powder, cinnamon, ginger, nutmeg, and salt. Gradually add the dry mixture to the wet ingredients, stirring until just combined.
**Scoop the Cookies:** Drop tablespoon-sized scoops of dough onto the prepared cookie sheet, spacing them about 2 inches apart.
**Bake the Cookies:** Bake for 10-12 minutes or until the edges are lightly golden and the cookies are set. Allow them to cool on the baking sheet for 5 minutes, then transfer to a cooling rack to cool completely.
**Prepare the Frosting:** While the cookies are cooling, make the frosting. Using an electric mixer, beat the cream cheese and butter together until smooth and fluffy. Gradually add the powdered sugar, vanilla extract, and cinnamon, and beat until creamy and well combined.
**Frost the Cookies:** Once the cookies are completely cooled, spread a generous amount of cinnamon cream cheese frosting on top of each cookie.
**Serve:** Serve immediately or store in an airtight container. Enjoy!