Brown the Butter: Melt half of the butter (½ cup, 113g) in a saucepan over medium heat, stirring frequently, until golden brown and nutty in aroma. Transfer to a large mixing bowl and let cool slightly.
Cream the Sugars and Butter: Add the remaining butter to the browned butter and stir to combine. Mix in the brown sugar and granulated sugar until smooth.
Incorporate Wet Ingredients: Beat in the eggs and egg yolk, one at a time, then mix in the vanilla extract.
Combine Dry Ingredients: In a separate bowl, whisk together the flour, baking soda, cornstarch, and salt. Gradually add to the wet mixture, mixing until just combined.
Add Mix-ins: Fold in the chocolate chips and walnuts, if using.
Chill the Dough: Cover and refrigerate for at least 30 minutes, or up to 24 hours for deeper flavor and better texture.
Preheat and Prepare: Preheat the oven to 375°F (190°C) and line baking sheets with parchment paper.
Portion and Bake: Scoop dough into 3-tablespoon portions and place on the prepared baking sheets, spacing them about 3 inches apart.
Bake: Bake for 11-14 minutes, until the edges are golden brown but the centers still look slightly underbaked.
Cool and Enjoy: Let cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.