In a medium saucepan over medium-low heat, melt the unsalted butter, stirring frequently to prevent burning. Watch as it transforms from melted to golden brown in about 5-7 minutes, releasing a nutty aroma. Once browned, remove it from the heat and let it cool slightly while you gather the other ingredients.

In a mixing bowl, combine the browned butter with the light brown sugar and granulated sugar. Use a spatula to mix until well blended. Add in the large egg, egg yolk, and vanilla extract, stirring until everything is smoothly combined and the mixture appears creamy and glossy.

Sift in the all-purpose flour, baking soda, and kosher salt into the wet mixture. Gently fold the dry ingredients into the wet mixture until no flour streaks remain. Be cautious not to overmix.

Once the dough is combined, fold in the chocolate chips, ensuring the chocolate is evenly distributed throughout the dough.

Cover the bowl with plastic wrap and refrigerate the cookie dough for at least 1 hour, or preferably overnight.

Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper. Using a cookie scoop, drop rounded tablespoons of dough onto the prepared sheets, leaving about 2 inches of space between each cookie.

Slide the baking sheets into the preheated oven and bake the cookies for 12-13 minutes, until puffed and golden brown around the edges but soft in the center. Sprinkle with flaky sea salt before removing.

Allow the cookies to cool on the baking sheets for about 5 minutes before transferring them to a wire rack to cool completely.