Preheat oven to 350°F.
Add butter to a small saucepan; cook over medium heat until brown, bubbly and little bits on the bottom of pan (approximately 5-6 minutes or longer, depending on stove top). Allow to cool.
Whisk the flour, baking soda, pumpkin spice mix, and salt together in a medium bowl. Set aside.
In a large bowl, combine brown sugar, granulated sugar, cooled brown butter, eggs, pumpkin puree, and vanilla. Using a wire whisk or a hand mixer, combine all of the wet ingredients until creamy and smooth, about 3-4 minutes if whisking by hand and 1-2 minutes if using an electric mixer.
Add the dry ingredients in batches to the butter-egg mixture and quickly mix until combined, making sure not to overmix. Mix in the oats and chocolate chips. Refrigerate cookie dough for 30 minutes or up to 2 days.
Preheat oven to 350°Fahrenheit.
Line 3 baking sheet pans with parchment paper. Using an ice cream scooper, scoop 6 cookie dough balls on each sheet pan. Sprinkle the flaky salt over each cookie.
Place sheet pans in the oven and bake for 7 minutes. Remove one pan at a time from the oven and carefully give it a quick bang on the counter (to flatten out cookies) and place back in the oven to continue baking for an additional 6 minutes or so, about 13 minutes in total, or until lightly golden brown. Remove from oven, cool, and enjoy!