In a large bowl, beat the cold cubed butter with the white sugar and brown sugar using an electric mixer on medium speed until completely blended, about 3 to 5 minutes. Scrape down the sides, then add the eggs one at a time, beating well after each addition.

In a separate bowl, spoon the flour into a dry measuring cup and level it off for an accurate measure. Add the baking soda, cornstarch, and fine salt, then whisk until thoroughly combined.

Add the dry mixture to the butter-sugar mixture all at once and mix until just combined. Do not overmix. Fold in both chocolate chips until evenly distributed, cover the bowl, and refrigerate the dough for 30 minutes.

Position a rack in the middle of the oven and preheat to 400 degrees F. Line a light colored baking sheet with parchment paper.

Scoop the chilled dough into 6-ounce portions. Place 2 to 3 dough balls 6 to 8 inches apart on the prepared baking sheet and sprinkle each with a generous pinch of flaky or coarse salt. Bake for 12 to 15 minutes until the edges are golden brown and the centers are just set. Let the cookies cool on the pan for 5 minutes, then transfer the entire parchment sheet with cookies to a wire rack. Keep the remaining dough refrigerated while baking in batches.

Store the cookies in an airtight container at room temperature for up to 3 days. For a warm treat, microwave a cookie for about 15 seconds before serving.