Brown your butter on medium heat until you start to see brown specs in the pot and smell a nutty aroma. By browning the butter you are toasting the milk solids in the butter. Be careful not to burn the milk solids.
Allow the butter to cool and place in the fridge until it starts to solidify but is still soft.
In a small bowl, whisk together flour, baking soda, and salt.
In a medium bowl, cream together the softened brown butter, granulated sugar, and brown sugar until smooth and fluffy.
Beat in the egg yolk and vanilla extract.
Stir in the dry ingredients until just combined. Fold in chocolate chips.
Preheat oven to 375°F (190°C). Line a baking sheet with parchment paper.
Scoop 6 equal-sized balls of dough and place them 2 inches apart on the baking sheet.
Bake for 9–11 minutes, until the edges are lightly golden and the centers are still soft.
Cool on the baking sheet for 2 minutes, then transfer to a wire rack to cool fully.