Place butter in a light-colored saucepan over medium heat. Melt completely, then continue cooking while whisking constantly. The butter will foam, then subside, and eventually turn a rich amber color with a nutty aroma (approximately 5-7 minutes). Small brown specks will appear at the bottom of the pan. Immediately transfer to a heat-proof bowl and let cool for 10 minutes.
Add brown sugar and granulated sugar to the cooled brown butter and whisk until fully combined. The mixture won't be as fluffy as traditional creamed butter and sugar—this is perfectly normal.
Whisk in the pumpkin puree, egg, egg yolk, and vanilla extract until smooth.
In a separate bowl, whisk together flour, pumpkin pie spice, baking soda, and salt until evenly distributed.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined.
Fold in the chocolate chips by hand. The dough will be slightly sticky but manageable.
Cover the dough and refrigerate for at least 60 minutes.
Preheat your oven to 350°F (175°C) and line baking sheets with parchment paper.
Scoop chilled dough into 2-tablespoon portions and roll into balls. Place on the prepared baking sheets, leaving 2 inches between cookies.
Press a few extra chocolate chips on top of each dough ball.
Bake for 12-14 minutes until edges are set but centers remain soft. The cookies will look slightly underbaked in the center—this is correct and ensures a soft, chewy texture.
Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely. The cookies will continue to set as they cool.