Begin by creaming the cubed unsalted cold butter with brown and granulated sugars in a large mixing bowl. Use a hand mixer or stand mixer on medium speed for about 4-5 minutes until the mixture is light and fluffy. Next, add the cold eggs one at a time, mixing well after each addition and scraping down the sides to ensure an even combination.

In a separate large bowl, whisk together the all-purpose flour, cornstarch, baking powder, baking soda, and salt until fully combined. Gradually incorporate this dry mixture into the wet ingredients from Step 1 while mixing on low speed. Continue mixing until a thick dough forms, ensuring not to overmix to maintain the desired texture of your Levain-Style Two-Chip Chocolate Chip Cookies.

Gently fold in both the semi-sweet and milk/white chocolate chips, making sure they are evenly distributed throughout the thick dough. If you're using chopped walnuts or pecans for added texture, include them during this step as well. This will create a delightful balance of flavors in each cookie, contributing to their gooey goodness.

Divide the dough into 8-10 large balls, weighing approximately 6 ounces each. Keep each ball tall and rugged rather than flattening them, as this will help achieve that iconic Levain look. For enhanced flavor and texture, you can chill the shaped dough balls in the refrigerator for 30-60 minutes before baking if you have the time.

Preheat your oven to 400°F (205°C) and prepare baking sheets with parchment paper or silicone mats. Place 3-4 dough balls per tray, making sure to space them appropriately. Bake for 9-11 minutes or until the edges turn golden brown and the centers appear slightly underdone. This method ensures that your Levain-Style Two-Chip Chocolate Chip Cookies have that perfect gooey center.

Remove the cookies from the oven and allow them to cool on the baking sheet for about 10 minutes. This resting period allows them to firm up a little more while retaining their wonderful softness. After cooling, gently transfer the cookies to a wire rack to cool completely, ensuring they maintain their delicious texture.