In a light-colored pan, melt the butter over medium-high heat.
Stir frequently for 4-5 minutes until golden brown bits form at the bottom.
Immediately remove from heat and transfer to a bowl to cool for 20-30 minutes.
Preheat oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a mixing bowl, whisk together cooled brown butter, granulated sugar, and brown sugar until light and fluffy.
Mix in the egg until fully incorporated, then add the egg yolk and vanilla extract.
In a separate bowl, whisk together flour, salt, and baking soda.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined (avoid over-mixing).
Fold in the chopped pecans.
Scoop 2 tablespoons of dough, roll into balls, and place on the baking sheet.
Bake for 9-10 minutes until edges are golden brown but centers remain soft.
Let cookies cool on the baking sheet for 3-4 minutes before transferring to a wire rack.