Preheat your oven to 350°F.
In a small bowl, whisk together the all-purpose flour, baking soda, and salt.
Over medium heat, melt the butter in a pan. Let it cook for about 5 to 6 minutes until it turns a beautiful brown color. Be careful not to overcook it. Transfer the browned butter to a bowl and let it cool.
In a large mixing bowl, combine the brown sugar, granulated sugar, and browned butter. Mix until just combined. Then, add the egg, egg yolks, and vanilla extract. Whisk until the mixture becomes smooth and thick.
Gradually add the dry ingredients to the wet ingredients, folding them in gently with a rubber spatula until a cookie dough forms.
Stir in the milk chocolate chips and semi-sweet chocolate chunks. Let the dough rest for about 15 to 20 minutes.
Line a baking sheet with parchment paper.
Scoop out portions of the dough, about the size of a 1/4 to 1/3 measuring cup, and place them on the baking sheet. Make sure to leave enough space between each cookie (about 6 cookies per sheet).
Bake in the preheated oven for approximately 10 minutes, until the edges turn golden brown and the center is still slightly soft. Remember, the cookies will continue to bake on the hot pan out of the oven.
Allow the cookies to cool on the pan for about 10 minutes until they firm up before transferring them to a cooling rack to finish cooling. Then, enjoy your freshly baked cookies!