Prep the pans. Line two baking sheets with parchment paper or silicone mats. Set them nearby so you can drop the cookies while the mixture is still warm.
Melt the base. In a medium saucepan over medium heat, combine the butter, brown sugar, and milk. Stir constantly until the butter melts and the mixture begins to bubble, about 3 4 minutes.
Boil briefly. Once it reaches a full rolling boil, set a timer for 1 minute. Keep stirring so the sugar dissolves completely and the mixture thickens slightly. Do not walk away this short boil is what helps the cookies set.
Stir in pumpkin and flavor. Remove the pan from heat. Immediately stir in the pumpkin puree, vanilla, pumpkin pie spice, cinnamon, and salt until smooth and fragrant. The mixture will look glossy and smell like warm fall spices.
Fold in the oats. Add the oats all at once. Stir firmly until every flake is coated and the mixture pulls away from the sides of the pan. It should look thick and sticky. If using chocolate chips or nuts, fold them in now while the mixture is still warm.
Portion the cookies. Working quickly, drop rounded tablespoons of the mixture onto the prepared sheets. Space them about 1 inch apart. Gently press the tops with the back of a spoon if you prefer flatter cookies.
Cool and set. Let the cookies sit at room temperature for 20–30 minutes until firm to the touch. For faster results, place the sheets in the refrigerator for 15 minutes. Once set, they hold their shape and are ready to eat.
