In a medium saucepan, melt the butter over medium heat. Continue to cook, stirring frequently, until the butter turns golden brown and has a nutty aroma. This should take about 5-7 minutes. Be careful not to burn it! Once browned, remove from heat and let it cool for 10-15 minutes.
Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone baking mats.
In a large mixing bowl, add the browned butter, brown sugar, and granulated sugar. Use an electric mixer to beat them together until smooth and creamy, about 2-3 minutes.
Add the egg, egg yolk, and vanilla extract to the bowl. Beat on medium speed until fully combined and smooth.
In a separate bowl, whisk together the flour, baking soda, and salt.
Gradually add the dry ingredients to the wet mixture, mixing on low speed until just combined. Be careful not to overmix.
Using a spatula or wooden spoon, fold in the old-fashioned oats, quick oats, and chopped semi-sweet chocolate until evenly distributed throughout the dough.
Scoop about 1.5 tablespoons of dough and roll into balls. Place them on the prepared baking sheets, spacing them about 2 inches apart to allow for spreading.
Bake the cookies for 10-12 minutes, or until the edges are golden brown and the centers look slightly underbaked. The cookies will continue to set as they cool.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely. Enjoy these deliciously chewy brown butter oatmeal chocolate chip cookies.
