Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper.
In a medium saucepan, melt the butter over medium heat. Continue cooking, stirring frequently, until the butter turns golden brown and has a nutty aroma (about 5-7 minutes). Be careful not to burn it. Once browned, remove from heat and let it cool slightly.
In a large mixing bowl, combine the brown sugar and granulated sugar. Pour in the brown butter, and mix until well combined.
Add the eggs, one at a time, mixing well after each addition. Stir in the vanilla extract.
In a separate bowl, whisk together the flour, baking soda, and sea salt. Gradually add this dry mixture to the wet ingredients, stirring until just combined.
Fold in the chocolate chunks and walnuts (if using) until evenly distributed throughout the dough.
Using a cookie scoop or tablespoon, scoop out balls of dough and place them about 2 inches apart on the prepared baking sheets.
Bake in the preheated oven for 10-12 minutes, or until the edges are golden and the centers look slightly underbaked.
Remove from the oven and let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
Notes
Arrange the cookies on a decorative plate, dust with a little sea salt for a gourmet touch, and serve with a glass of milk!