Prepare the Butter: In a large bowl, cream together the cold, cubed butter and both sugars using an electric mixer until light and fluffy, approximately 3-5 minutes. The cold butter is crucial for that signature Levain Two Chip Cookies texture.
Incorporate Wet Ingredients: Beat in the cold eggs one at a time, then stir in the vanilla extract.
Combine Dry Ingredients: In a separate bowl, whisk together the flour, baking soda, baking powder, and salt.
Combine Wet and Dry: Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Be careful not to overmix.
Add Chocolate: Gently fold in the dark chocolate chunks and milk chocolate chips. Ensure they are evenly distributed throughout the dough.
Chill the Dough: Cover the dough and refrigerate for at least 1 hour, or preferably overnight. This allows the flavors to meld and prevents the cookies from spreading too much during baking. This chilling step is key to achieving the perfect Levain Two Chip Cookies texture.
Preheat Oven: Preheat oven to 410°F (210°C). Line a baking sheet with parchment paper.
Shape the Cookies: Scoop out 6 large mounds of dough (about 6 ounces each). Gently form them into tall, round shapes. Do not flatten them! This is crucial for achieving that signature Levain Bakery look.
Bake: Place the cookies on the prepared baking sheet, leaving plenty of space between each cookie. Bake for 9-12 minutes, or until the edges are golden brown and the centers are slightly underbaked. Remember, slightly underbaked is what makes these Levain Two Chip Cookies so delicious!
Cool: Let the cookies cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely (or enjoy warm!).