Using a stand mixer fitted with the paddle attachment, beat the butter on low speed until smooth, 1 to 2 minutes.
Add the sugars and beat on medium-high speed until creamed and well combined, about 3 minutes.
Stop, scrape down the sides of the bowl, and add the egg, vanilla, and beat on medium-high speed until light and fluffy, about 3 minutes.
Stop, scrape down the sides of the bowl, and add the flours, corn starch, baking soda, salt, and mix until just combined, about 1 minute.
Add the chocolate chips and chunks, and either fold in by hand or beat for a few seconds on low speed.
Using a 2-ounce cookie scoop, form heaping mounds weighing 2 1/4-ounces each (weighed on a scale, which is approximately a scant 1/4-cup measure. Dough mounds will look large for their weight because there's lots of chocolate pieces adding bulk). Place mounds on a large plate or tray, cover with plasticwrap and refrigerate for at least 2 hours, up to 5 days.
Preheat oven to 350 F, line a baking sheet with nonstick baking mat, parchment, or spray with cooking spray. Place dough on the baking sheet, spaced at least 2 inches apart I bake 8 cookies per sheet. Bake for 8 to 10 minutes, until barely golden brown around the edges. Center should still be slightly gooey.Tops will not be browned and will be pale. Do not cook longer than ten minutes as cookies will darken and firm up as they cool. Rotate half way through baking time if desired.
Allow cookies to cool on the baking sheet for 5 minutes before removing and transferring to a rack to finish cooling. Store cookies in an airtight container at room temperature for up to 5 days or in the freezer for up to 3 months. Alternatively, unbaked cookie dough can be stored in an airtight container in the refrigerator for up to 5 days, so consider baking only as many cookies as desired and save the remaining dough to be baked in the future when desired.