Get things started by preheating your oven to 350°F (175°C). This helps your cookies bake just right.
In a bowl, mix the softened butter and granulated sugar until they're all fluffy. Then, toss in the egg, pumpkin puree, and vanilla extract. Mix it up until everything's happy together.
Grab another bowl and whisk together the flour, quick-cooking oats, baking soda, ground cinnamon, ground nutmeg, and salt. This is gonna be your dry mix.
Slowly mix your dry mix into your wet mix. Keep mixing until they make a cool dough that's soft and a bit sticky.
Use a cookie scoop or spoon to plop bits of dough onto baking sheets lined with parchment paper. Leave a little space between them.
Slide those baking sheets into your preheated oven and let the cookies bake for around 12-15 minutes. They'll turn a nice golden brown at the edges, and your kitchen's going to smell amazing!
Once they're baked, let the cookies chill on the baking sheets for a bit. Then, move them onto a wire rack to cool down. That way, they'll get all nice and chewy.