Sift flours, baking soda, baking powder, and salt into a bowl.
Using a mixer fitted with the paddle attachment, cream butter, and sugars together until very light and fluffy, for about 5 minutes. Add eggs, one at a time, mixing well after each addition. Beat in the vanilla.
Reduce the speed to low. Add the dry ingredients and mix until just combined 5 to 10 seconds.
Add the chocolate pieces and fold them into the batter, being careful not to break them. Press plastic wrap against the dough and refrigerate for 24 to 36 hours. Dough may be used in batches and can be refrigerated for up to 72 hours.
Move the oven rack to the middle position and preheat oven to 350°F. While the oven preheats, take the dough out of the refrigerator.
Line rimmed baking sheets with parchment paper or a nonstick baking mat.
Scoop mounds of dough the size of generous golf balls (or use a #16, 4 Tablespoon scoop) onto the prepared baking sheets, leaving 2 ½-3 inches between mounds. Sprinkle lightly with sea salt.
Bake one cookie sheet at a time until cookies are golden brown but still soft, 18 to 20 minutes.
Transfer the sheet to a wire rack to cool for 10 minutes, then slip the cookies onto another rack to cool for another 30 minutes.