In a large mixing bowl, use an electric mixer to cream together the butter, sugar, and brown sugar until light and fluffy. Add the egg and vanilla extract, then beat until fully combined.
In a separate bowl, whisk together the flour, baking soda, salt, cinnamon, cloves, ginger, and nutmeg. Stir in the quick oats.
Gradually add the dry ingredients to the butter mixture, alternating with the pumpkin puree. Stir until just combined. If using optional mix-ins like chocolate chips, nuts, or dried fruit, fold them into the dough.
Cover the dough with plastic wrap and chill in the refrigerator for at least 30 minutes (or up to 1 day).
Preheat the oven to 350°F (175°C) and line baking sheets with parchment paper or silicone mats.
Using a 1 ½-tablespoon cookie scoop, drop portions of dough onto the prepared baking sheets, spacing them about 2 inches apart. Gently press down on each dough mound using the bottom of a measuring cup or fork tines to flatten them slightly.
Bake for 12–17 minutes, or until the edges are lightly golden and the tops are set (not shiny). Do not overbake, as you want them soft and chewy.
Remove from the oven and let the cookies cool on the baking sheet for 5 minutes. Then, transfer them to a wire rack to cool completely.