Step 1: Brown the Butter. Place the butter in a medium saucepan over medium heat. Melt the butter, then continue to cook while whisking constantly. The butter will foam, then turn a golden brown color with a nutty aroma. Once you see brown bits at the bottom, remove from heat immediately and pour into a large bowl to cool for 15 minutes.
Step 2: Toast the Pecans. While the butter cools, place the chopped pecans in a dry skillet over medium heat. Toast them for 3 to 5 minutes, stirring frequently, until they are fragrant and slightly darker. Set them aside to cool.
Step 3: Mix the Dry Ingredients. In a medium-sized bowl, whisk together the all-purpose flour, baking soda, and sea salt. Ensuring these are well-combined helps the cookies rise evenly and prevents salt pockets.
Step 4: Combine Butter and Sugars. Add the brown sugar and granulated sugar to the cooled brown butter. Whisk vigorously for about 2 minutes until the mixture is smooth and the sugar begins to dissolve into the fat.
Step 5: Add Wet Ingredients. Add the whole egg, the extra egg yolk, and the vanilla extract to the butter mixture. Whisk until the batter looks pale and creamy. The extra yolk adds a wonderful chewiness to the final cookie.
Step 6: Fold in Dry Ingredients. Gradually add the flour mixture to the wet ingredients. Use a spatula to fold the dough together until just a few streaks of flour remain. Do not overmix, as this can make the cookies tough.
Step 7: Add Mix-ins and Chill. Fold in the toasted pecans and chocolate chips until evenly distributed. For the best flavor and texture, cover the dough and chill in the refrigerator for at least 30 minutes (or up to 24 hours).
Step 8: Scoop and Bake. Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper. Scoop rounded tablespoons of dough onto the sheet, spacing them 2 inches apart. Bake for 10 to 12 minutes until the edges are golden but the centers still look slightly soft. Sprinkle with flaky salt if desired.