Preheat the oven to 375°F. Line 2 baking sheets with parchment paper.
To make the dough: In the bowl of a stand mixer fitted with the paddle attachment, add the butter, cane sugar, and dark brown sugar. Mix on low until there are no butter chunks. Add the egg and pumpkin puree and mix just slightly, enough to break the yolks.
In a separate bowl, add the dry ingredients: flour, pumpkin spice, cinnamon, vanilla bean, baking soda, and sea salt and whisk together.
Add to the butter mixture and mix on low until almost combined, you’ll see bits of flour. Add the pecans and mix on low until fully combined.
Using your hands, form the dough into 24 balls and place them on the prepared baking sheets. Flatten them so they are disks that are about 2 ¼-inch in diameter.
Bake for 11 minutes or until set and dry. Let cool completely on the cookie sheet.
Store in an airtight container for up to 7 days.
To make the frosting: In the bowl of a stand mixer fitted with the paddle attachment, add the butter, powdered sugar, and milk. Mix on low until combined and then speed mixer up to high and mix for 1 to 2 minutes or until light and fluffy.
Using a butter knife, frost each cookie.
Store in an airtight container for up to 7 days.