Preheat the oven to 350°F (175°C).

In a large mixing bowl, cream together the softened butter, brown sugar, and granulated sugar until light and fluffy.

Add the egg and vanilla extract to the creamed mixture, mixing until well combined.

In another bowl, whisk together the pumpkin puree, baking soda, spices, salt, and rolled oats.

Gradually add the pumpkin mixture to the butter mixture, mixing until just combined.

Scoop tablespoon-size amounts of dough and place them onto a lined baking sheet.

Bake in the preheated oven for 10-12 minutes, or until the edges are lightly browned.

Remove cookies from the oven and let them cool on the baking sheet for 5 minutes before transferring to a wire rack.

In a separate bowl, mix the powdered sugar, maple syrup, and milk to create the frosting.

Frost the cooled cookies with the maple frosting.