In a medium saucepan, melt the 2 sticks of salted butter over medium heat. Stir frequently until the butter starts to bubble and foam. Continue cooking until the butter turns a golden brown color and releases a nutty aroma. This usually takes about 5-7 minutes. Remove from heat and let it cool slightly.
In a large mixing bowl, combine the brown butter, brown sugar, eggs, and vanilla extract. Whisk together until the mixture is smooth and glossy.
In another bowl, whisk together the all-purpose flour, old-fashioned oats, baking soda, and kosher salt until evenly mixed.
Gradually add the dry ingredients to the wet ingredients, using a spatula to fold them together. Be careful not to overmix; the dough should be just combined.
Gently fold in the chocolate chunks or chips until evenly distributed throughout the dough.
For best results, cover the dough with plastic wrap and chill in the refrigerator for at least 30 minutes.
While the dough is chilling, preheat your oven to 350°F (175°C) and line your baking sheets with parchment paper.
Once the dough has chilled, use a cookie scoop or tablespoon to drop rounded balls of dough onto the prepared baking sheets, leaving about 2 inches of space between each cookie.
Bake in the preheated oven for 10-12 minutes, or until the edges are golden brown but the centers are still soft. Remove from the oven and sprinkle with flaky sea salt, if desired.
Allow the cookies to cool on the baking sheets for 5 minutes before transferring them to a cooling rack. Enjoy warm or at room temperature!
