Preheat oven to 350°F.
In a small bowl, whisk together all purpose flour, baking soda, and salt.
To a pan over medium heat, add the butter. Cook for 5 to 6 minutes until it starts to bubble and then brown. Make sure not to cook it any further or it can burn. Transfer it to a bowl and allow it to cool so it's not hot.
In a large mixing bowl, add the brown sugar and white sugar. Pour in the butter and mix just until combined. Then add the egg and egg yolks and vanilla extract. Whisk until smooth and thick.
Add the dry to the wet and fold in using a rubber spatula until a cookie dough forms.
Mix in the milk chocolate and dark chocolate and let the dough rest for 15 to 20 minutes.
Line a sheet pan with parchment paper.
Scoop out portions of the dough about the size of 1/4 to 1/3 measuring cup. Make sure to space them apart, 6 cookies per sheet.
Pop in the oven to bake for about 10 minutes until the edges are golden brown and the center is still a bit soft. The cookies will continue baking out of the oven on the hot pan.
Leave them on the pan for about 10 minutes or until firm before transferring them to a cooling rack to finish cooling and enjoy!