Cut the butter into even pieces and melt it in a light-colored skillet over medium heat. Keep stirring as it foams and the milk solids start browning on the bottom. Once it turns golden amber and smells nutty, pull it off the heat immediately.
Pour the browned butter, including all those browned bits, into a heatproof bowl. Let it cool for about 10 minutes, then refrigerate until solid, roughly 90 minutes. This step is essential for structure.
Once solid, beat the brown butter on high speed until smooth and creamy, even if it looks grainy at first. Add both sugars and beat until light and fluffy, about 2 minutes total.
Mix in the egg, egg yolk, and vanilla extract until fully combined. Scrape down the sides of the bowl so everything blends evenly without any streaks.
In a separate bowl, whisk together the flour, cornstarch, baking soda, and salt. This keeps the leavening evenly distributed before it hits the wet mixture.
Add the dry mix to the wet ingredients on low speed until just combined. Drizzle in the milk while mixing, then fold in the chocolate chips until they're evenly spread through the dough.
Scoop the dough into 2-tablespoon portions and shape them tall rather than wide. Refrigerate for at least 2 hours; this keeps the cookies thick instead of letting them spread thin.
Bake at 375°F for 12-14 minutes until the edges turn golden but the centers still look soft. Let them cool on the sheet for 5 minutes before moving to a wire rack.