In a medium saucepan, melt the butter over medium-low heat. As the butter melts, it’ll start to foam, then turn a clear golden color. Continue to stir the butter, scraping up any browned specks from the bottom of the pan as it starts to brown. It should have a nutty aroma. Once browned and nutty, remove from the heat; set aside to cool.
Whisk the flour, baking soda, salt, cornstarch, and spices together in a medium bowl; set aside.
In a stand mixer fitted with the paddle attachment, beat the browned butter and both sugars together on medium speed until smooth and incorporated, about 1 minute. Add the pumpkin puree and vanilla and continue beating until combined, using a rubber spatula to scrape down the sides of the bowl as needed. Add the dry ingredients and mix on low until just incorporated. Stir in the chocolate chips with a wooden spoon. Cover, and refrigerate dough for at least two hours, or up to three days.
Preheat the oven to 350ºF and line a baking sheet with parchment paper. Roll the dough into balls about the size of a golf ball, then place them on the baking sheet about 2 inches apart. Flatten each dough ball slightly so that it resembles a little hockey puck.
Bake for 8-10 minutes, or until the edges are set and the centers are puffy but still look slightly underdone. If desired, immediately press more chocolate chips into the tops of each the cookie. Allow cookies to cool on the baking sheet for 10 minutes before transferring to a wire rack to cool completely.