Step 1: Brown the Butter
1. In a medium saucepan over medium heat, melt the butter. Continue cooking, stirring frequently, until the butter turns golden brown and develops a nutty aroma, about 5-7 minutes. Be careful not to burn it.
2. Remove from heat and let the brown butter cool slightly.

Step 2: Mix the Cookie Dough
1. In a large mixing bowl, combine the brown butter, brown sugar, and granulated sugar. Mix until well combined.
2. Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
3. In a separate bowl, whisk together the flour, baking soda, and salt.
4. Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Gently fold in the chocolate chips.

Step 3: Chill the Dough
1. For best results, cover the dough and refrigerate for at least 30 minutes. This helps the flavors develop and prevents the cookies from spreading too much.

Step 4: Bake the Cookies
1. Preheat your oven to 350°F (175°C).
2. Line a baking sheet with parchment paper. Using a cookie scoop or tablespoon, drop rounded balls of dough onto the baking sheet, leaving space between each cookie.
3. Bake for 10-12 minutes, or until the edges are lightly golden and the centers are still soft. Remove from the oven and let cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.

Step 5: Serve
1. Serve warm or at room temperature. Enjoy your delicious Brown Butter Chocolate Chip Cookies!