Melt the butter in a light-colored saucepan over medium heat, swirling often, for 5-7 minutes until it foams and turns golden with nutty brown bits at the bottom. Pour it into a large bowl, including the brown bits, and cool for 10 minutes.
Spread the pumpkin puree on a double layer of paper towels and press another paper towel on top to soak up the excess moisture. This is the secret to chewy pumpkin cookies instead of cakey ones.
Whisk the brown sugar and granulated sugar into the browned butter until smooth. Whisk in the blotted pumpkin and vanilla.
In a separate bowl, whisk together the flour, pumpkin pie spice, cinnamon, baking soda and salt. Stir into the pumpkin mixture just until combined, then fold in the chocolate chips.
Cover and chill the dough for 30 minutes. Near the end, preheat the oven to 350°F and line two baking sheets with parchment paper.
Scoop the dough into 2 tbsp mounds, place them 2 inches apart and flatten each one slightly, since these cookies don't spread much.
Bake for 11-13 minutes, until the edges are set and lightly golden and the centers look just done.
Cool on the baking sheet for 10 minutes, then transfer to a wire rack. Makes about 18 cookies.