Preheat the oven to 350 degrees F and line two large baking sheets with parchment paper.
Add the softened butter and brown sugar to the bowl of a stand mixer fitted with the paddle attachment. Beat on medium speed for 1-2 minutes, or until the mixture is light and fluffy.
Next add the egg, pumpkin puree, and vanilla. Mix to combine and scrape down the sides of the bowl as needed.
In a medium bowl, combine the oats, flour, baking soda, pumpkin pie spice, and kosher salt.
With the mixer on low speed, slowly add the dry ingredients to the wet. Mix just until the dry ingredients are incorporated– you don’t want to overmix!
Scoop out 1.5 tablespoon-sized portions and place them at least 2” apart on the parchment-lined baking sheets.
Bake for 12-14 minutes or until the cookies are set and beginning to brown around the edges. Immediately when you remove the cookies from the oven, tap the tray on the counter a few times– this will help sink the centers so the cookies become soft and chewy.
Allow the cookies to cool completely on the pan and then transfer them to an airtight container. Store at room temperature for up to three days.