Melt the butter in a saucepan over medium heat until golden brown.
Remove from heat and let cool slightly.
Mix brown sugar and granulated sugar in a bowl.
Add the brown butter and mix until combined.
Stir in the egg and egg yolk until smooth.
Add vanilla extract and mix well.
Combine flour, baking soda, and salt in another bowl.
Gradually add dry ingredients to the wet ingredients, mixing until just combined.
Fold in chocolate chips until evenly distributed.
Scoop dough onto baking sheets and bake at 350°F (175°C) for 10-12 minutes.
Let cool on the baking sheet before transferring to a wire rack.