Cut the butter into small pieces and place in a light-colored skillet. The pale pan helps you see when the butter turns golden. Melt over medium heat, stirring or whisking constantly. Once melted, the butter will foam; keep stirring. After 5 to 7 minutes, the butter will start to brown and you will see tiny brown specks (toasted milk solids) form on the bottom. When it turns a rich golden color, immediately remove from heat and pour into a heatproof bowl, scraping in all the browned bits. Let cool for 10 minutes, then refrigerate until solid, about 90 minutes. After 30 minutes, cover the bowl tightly.

Once the brown butter is fully solid, scoop it into a large mixing bowl or the bowl of a stand mixer. Using a hand mixer or the paddle attachment, beat on high speed for 1 to 2 minutes until smooth and creamy. It may look grainy at first but will come together. If the butter is too firm to cream, let it sit at room temperature for 5 to 10 minutes, or microwave for 5 to 8 seconds until just softened—do not melt it.

Add the brown sugar and granulated sugar, then beat on medium-high speed until the mixture is lighter in color and well combined, about 2 minutes. Add the egg, egg yolk, and vanilla extract, beating until incorporated. Scrape down the sides and bottom of the bowl as needed.

In a separate bowl, whisk together the flour, cornstarch, baking soda, and salt. Add the dry ingredients to the butter mixture and mix on low speed until just combined. With the mixer running on low, drizzle in the milk and mix until incorporated. The dough will be thick and soft. Add the chocolate chips and mix until evenly distributed.

Scoop and roll the dough into balls, using about 2 tablespoons or 45g each. Shape them tall rather than wide—almost like a cylinder—to help the cookies bake up thick. Place the dough balls on a lined baking sheet or plate, cover, and refrigerate for at least 2 hours or up to 3 days.

Preheat the oven to 375°F (191°C). Line large baking sheets with parchment paper or silicone baking mats. Arrange 8 dough balls per sheet, spacing them about 3 inches apart. If using, sprinkle flaky sea salt on top of each dough ball.

Bake for 12 to 14 minutes, until the edges are lightly golden brown. The centers will look soft when you pull them out. Let the cookies cool on the baking sheet for 5 minutes. During this time, you can press a few extra chocolate chips into the tops for looks. The cookies will settle slightly as they cool. After 5 minutes, transfer to a wire rack to cool completely.

Store the cookies in an airtight container at room temperature for up to 5 days.