Preheat oven to 350°F (175°C).
In a saucepan, melt butter over medium heat until it turns golden brown. Let it cool.
In a bowl, mix pumpkin puree, brown sugar, and granulated sugar.
Add the egg and vanilla extract to the pumpkin mixture.
In another bowl, combine flour, oats, baking soda, cinnamon, nutmeg, and salt.
Pour the cooled brown butter into the pumpkin mixture and stir.
Gradually add the dry ingredients to the wet ingredients.
Fold in chocolate chips if using.
Drop spoonfuls of dough onto a baking sheet.
Bake for 10-12 minutes until edges are golden.
Let cookies cool on a wire rack.