Start by placing the unsalted butter in a saucepan over medium heat. Stir it continuously as it melts, watching for it to turn golden brown and develop a nutty aroma. This should take about 5-7 minutes. Once browned, remove from heat and let it cool slightly.
In a mixing bowl, combine the browned butter, brown sugar, granulated sugar, and vanilla extract. Use your mixer to cream them together until light and fluffy. Add in the egg and mix until well combined.
In another bowl, whisk together the all-purpose flour, cornstarch, baking soda, and kosher salt. Gradually add the dry mixture to the wet ingredients, mixing just until combined. Be careful not to overmix.
Gently fold in the semi-sweet chocolate chips with a spatula until evenly distributed throughout the dough.
For the best texture, cover the dough and chill it in the refrigerator for at least 30 minutes. This helps the flavors meld and prevents the cookies from spreading too much while baking.
Preheat your oven to 350°F (175°C). Line your baking sheets with parchment paper.
Using a cookie scoop, portion out the dough and place it on the prepared baking sheets, leaving space between each cookie as they will spread. Top each cookie with a few extra chocolate chips and a sprinkle of flaky sea salt.
Bake the cookies for 10-12 minutes or until the edges are golden brown. The centers may look slightly undercooked, but they will continue to firm up as they cool.
Allow the cookies to cool on the baking sheet for about 5 minutes before transferring them to a wire rack to cool completely. Enjoy your Browned Butter Sea Salt Chocolate Chip Cookies warm, or store them for later!