Preheat oven to 350 degrees Fahrenheit. Grease a baking sheet, or line it with parchment paper or a silicone mat.
In a large bowl with a hand mixer or in the bowl of a stand mixer affixed with the paddle attachment, beat the butter and sugars on medium speed until well-blended, about one minute. Add the egg and beat until incorporated. Add the pumpkin puree and vanilla extract. Mixture may appear slightly curdled, but don't worry! It's all good. In a medium bowl, whisk together the flour, baking soda, salt, cinnamon, nutmeg, ginger, and cloves. With the mixer on slow speed, add the dry ingredients to the wet, and mix just until blended. Add the oats and mix just until incorporated - overmixing will lead to a tough cookie. Nobody likes tough cookies.
Scoop onto cookie sheet in three-tablespoon mounds (I use a 50 mm cookie scoop). Place about two inches apart.
Bake at 350 degrees for 10 - 12 minutes, until set and beginning to turn golden.
Let sit for 5 minutes then transfer to a cookie sheet to cool completely. They keep well at room temperature in an airtight container for 3 - 4 days, or freeze in a zipper bag for 1 - 2 months.