Line a baking sheet with parchment paper or a Silpat and set aside. (You can skip this step if you don't have either. It just makes it easier to remove the cookies after they are baked.)
In a medium sized mixing bowl, whisk together both flours, cornstarch, baking soda and salt. Set aside.
Add cold, cubed butter to the bowl of a stand mixer or to a large bowl using a hand mixer. Beat on medium speed until butter is light and creamy. Scrape down the sides of the bowl with a rubber spatula as needed.
Add sugar and brown sugar to butter and mix on medium speed until combined. Scrape down the sides of the bowl if needed.
Add eggs to the bowl with the sugars and butter. Mix on medium speed until just combined.
All at once, add flour mixture and both chocolate chips to the bowl with the sugars, butter and eggs. Beat on low speed until just mixed together. Do not overmix.
Chill cookie dough covered in the refrigerator for at least one hour.
Preheat oven to 400° F.
Remove dough from refrigerator and separate into 8 equal size balls. You can fit 4 cookies on one cookie sheet. I bake the batches separately.
With the palm of your hand, flatten each cookie a little.
Bake cookies for 10-13 minutes until they are just browning on the edges. Do not overbake.
Remove cookies from the oven and let cool on cookie sheet for at least 15 minutes.
Transfer cookies to a wire cooling grid to finish cooling. (Cookies are best eaten when they are warm and gooey!)