Brown the Butter: In a medium saucepan over medium heat, melt the butter. Stir frequently until it foams and turns a golden brown color, about 5-7 minutes. Remove from heat and let it cool slightly.
Mix Sugars: In a large mixing bowl, combine the brown butter, brown sugar, and granulated sugar. Beat with a mixer until well combined and smooth.
Add Eggs and Vanilla: Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
Combine Dry Ingredients: In a separate bowl, whisk together the flour, baking soda, and salt. Gradually add this dry mixture to the wet ingredients, mixing until just combined.
Fold in Chocolate Chips and Nuts: Gently fold in the chocolate chips and chopped walnuts (if using) until evenly distributed in the dough.
Chill the Dough: Cover the dough and refrigerate for at least 30 minutes to an hour; this helps to intensify the flavors and makes for a better texture.
Preheat Oven: Preheat your oven to 350°F (175°C) during the last 10 minutes of chilling.
Shape Cookies: Line a baking sheet with parchment paper. Scoop out tablespoon-sized balls of dough and place them a couple of inches apart on the baking sheet.
Bake: Bake for 10-12 minutes or until the edges are lightly golden and the centers are still soft. Remember that cookies will continue to cook slightly after removing them from the oven.
Cool: Allow cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
Notes
Serve warm with a glass of milk or display them on a beautiful platter with a sprinkle of sea salt on top for added contrast.