In a large saucepan, melt butter over medium heat. Whisk constantly as it foams and then turns a golden amber color, releasing a nutty aroma. Once browned, transfer to a bowl to cool for 10 minutes.
Using an electric mixer, blend the cooled brown butter with both sugars for 1 minute. Add in the egg, egg yolk, vanilla, and yogurt, mixing until well incorporated.
In a separate bowl, whisk together flour, baking soda, and salt. Gradually mix these dry ingredients into the wet mixture until just combined. Stir in the chocolate chips.
Refrigerate dough for at least 2 hours, or up to 24 hours for best results. Avoid rushing this step for the perfect cookie texture.
Once the dough is chilled, preheat your oven to 350°F and line a baking sheet with parchment paper. If the dough is too hard, let it thaw for 20 minutes before scooping.
Scoop 2 heaping tablespoons of dough or use a medium cookie scoop to form balls. Place them 2 inches apart on the baking sheet. Bake for 9-11 minutes until golden.
Let cookies sit on the baking sheet for 5 minutes, then sprinkle with sea salt. Transfer to a wire rack to cool completely.