Preheat your 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.
Beat in the egg and pumpkin puree, mixing until fully combined.
In a separate bowl, whisk together the flour, baking soda, spices, and salt.
Gradually add the dry ingredients to the wet mixture, mixing until just combined.
Fold in the rolled oats gently.
Drop spoonfuls of dough onto a parchment-lined baking sheet, spacing them about 2 inches apart.
Bake in the preheated oven for 10-12 minutes, or until the edges are lightly browned.
Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
While the cookies cool, prepare the maple frosting by whisking together powdered sugar, maple syrup, and milk until smooth.
Once the cookies are cool, frost them with the maple frosting using a spatula or knife.
Serve and enjoy your Pumpkin Oatmeal Cookies with Maple Frosting!