In a large mixing bowl, cream together the cubed unsalted butter, brown sugar, and granulated sugar using a hand or stand mixer on medium speed. Mix for approximately 3-4 minutes, or until the mixture appears pale and fluffy. Scrape down the sides of the bowl halfway through to ensure even blending.

Add the eggs, one at a time, to the butter and sugar mixture, beating well after each addition. Pour in the vanilla extract and mix for an additional minute. Scrape the sides of the bowl to ensure all ingredients are fully incorporated.

In a separate bowl, whisk together the all-purpose flour, cake flour, cornstarch, baking soda, and salt. Gradually add the dry ingredients into the wet mixture, mixing just until combined. Avoid overmixing to prevent tough cookies.

Gently fold in the milk chocolate chips and chunks using a spatula. Reserve a small handful of chocolate chips for pressing onto the top of the cookies before baking for a decorative finish.

For thicker cookies with a richer flavor, wrap the dough in plastic wrap and chill it in the refrigerator for at least one hour, or up to 48 hours. If baking immediately, proceed to the next step.

Preheat the oven to 395°F (200°C). Line a light-colored baking sheet with parchment paper for even baking.

Roll the cookie dough into 4-ounce balls (approximately the size of a golf ball). Place them onto the prepared baking sheet, leaving space between each for spreading. If desired, press the reserved chocolate chips on top of each dough ball for a bakery-style appearance.

Bake the cookies for 9-11 minutes, or until the edges are lightly golden while the centers remain slightly underbaked. The residual heat will continue to bake the centers as they cool.

Once out of the oven, lightly sprinkle the cookies with sea salt flakes for a sweet-salty contrast. Allow the cookies to rest on the baking sheet for 10 minutes before transferring them to a wire rack to cool completely.