Preheat the oven to 400 degrees. Line 3 large baking sheets with parchment paper.
In your mixer bowl, cream together the cold, cubed butter and both sugars for approximately 3 minutes.
Beat in the eggs and vanilla, one at a time, scraping down the sides in between.
In a separate bowl, whisk together the flour, cornstarch, baking soda and salt.
Add it to the creamed butter, sugar and egg mixture and mix until combined, scraping down as needed.
Mix in the chocolate chunks and chips.
Using a 2 Tbsp cookie scoop, scoop the dough on to the trays, about 2 inches apart. (Press extra chips in to the top if desired.)
Bake each tray for 8-9 minutes on the middle rack until the cookies are light golden brown on the top.
Remove from the oven and let the cookies sit on the trays for 10 minutes then transfer to cooling rack.