Preheat the oven to 350 degree F. Line two baking sheets with parchment paper and set aside.
In a medium-sized bowl, whisk together the flour, baking soda, salt, and spices. Set aside for a moment.
In the bowl of a stand mixer, cream the butter and sugars for 2 minutes, or until light and fluffy. Add the egg, vanilla extract, and pumpkin puree. Beat for an additional minute.
Little by little, add the dry ingredients. Mix until just combined, scraping down the sides of the bowl as needed.
After you take the cookies out of the oven, start on the frosting. In a medium sauce pan over medium heat, add the butter, cream, brown sugar, salt, and spices. Whisk occasionally, and heat until it comes to a boil. Allow it to boil for 1 minute, and then remove the pan from the heat.
Immediately whisk in the vanilla extract and powdered sugar, whisking until smooth. Whisk in the pecans.
Allow the frosting to sit for 5-10 minutes, or until it begins to thicken but is still spreadable. Spread on top of the warm cookies.