Preheat the oven: Preheat the oven to 375°F. Line baking sheets with parchment paper.
Brown the butter: In a skillet or saucepan, melt the butter over medium heat. Continue cooking and stirring until the butter turns amber and small brown specks appear on the bottom of the pan. This takes about 8 minutes. Be careful not to burn the butter. Pour the brown butter into a heatproof bowl and allow it to cool for about 10 minutes.
Mix the butter and sugars: In a large mixing bowl, whisk the brown butter, brown sugar, and granulated sugar together until smooth. If the butter is still hot, allow the mixture to sit for 3 minutes, then mix for another 30 seconds. Repeat this process two more times.
Add the eggs: Add the egg and egg yolk one at a time, mixing until smooth after each addition. Scrape down the sides of the bowl as needed.
Add the vanilla: Add the vanilla extract and mix until combined.
Add the dry ingredients: In a separate bowl, whisk together the flour, salt, baking soda, and cornstarch. Add the dry ingredients to the wet ingredients and gently mix with a rubber spatula until just combined. Be careful not to overmix.
Add the chocolate chips: Fold in the chocolate chips until evenly incorporated.
Portion the dough: Scoop about 3 tablespoons of dough and roll into balls. Place them on the prepared baking sheet about 2 inches apart.
Bake: Bake for 7–9 minutes, or until the edges are beginning to turn slightly golden while the centers still look soft.
Cool: Let the cookies cool on the baking sheet for 5–10 minutes before transferring them to a wire cooling rack.