Add the pumpkin spice to a large heat-safe mixing bowl and set aside.
Place the cubed butter into a large saucepan and set it over medium heat, stirring until melted.
When the butter begins to sputter, stir every ten seconds or so until it bubbles and begins to foam. Once you see brown bits floating in the butter and a nutty aroma is released, immediately remove the pan from the heat.
To stop the cooking process, pour the butter into the mixing bowl with the pumpkin pie spice, making sure to get all the browned bits from the bottom of the pan. Stir the butter and spices together until well incorporated, then set aside to cool to room temperature.
Add the pumpkin to the same pan from before, then set it over medium-high heat. Using a rubber spatula, stir the purée constantly until it thickens and reduces to ¼ cup, around 3 minutes. Scrape the pan-roasted pumpkin into a bowl and set aside to cool (you can also place the bowl in the fridge to speed up this process).
Once the brown butter has cooled to room temperature, add in the light brown sugar and whisk for 1-2 minutes until well combined. Beat in the eggs, vanilla extract, and cooled pumpkin.
Once the mixture is smooth, fold in the flour, baking soda, and salt. Just before the flour is fully combined, add in the chopped chocolate and mix until no more streaks of flour remain. Do not overmix.
Scoop the dough onto a baking sheet lined with wax or parchment paper (no need to space them apart). Cover the tray with plastic wrap and refrigerate for at least 30 minutes but up to 4-5 days. At this point, the cookie dough can be frozen.1
Preheat the oven to 375℉ and line a baking sheet with parchment paper.
When ready to bake, evenly space the cookie dough balls onto the baking sheet with a 2'' gap between each cookie. If desired, press the top of the dough with more chopped chocolate pieces.
Bake for 10-12 minutes, rotating the tray halfway through. Remove the cookies from the oven once the edges are golden brown and set, but do not overbake. The inside of the cookies should still be gooey, as they will continue to cook as they cool. Once out of the oven, sprinkle the cookies with flaky salt and allow to cool before serving.