Sift flours
Sift cake flour and bread flour through a fine-mesh strainer into a medium bowl or onto parchment. Set aside.
Cream butter and sugars
In a stand mixer with the paddle, combine butter, granulated sugar, brown sugar, vanilla, baking soda, and salt.
Mix on medium, scraping as needed, until pale and fluffy, about 5 minutes.
Mix in eggs
With mixer on medium, add eggs one at a time, fully incorporating the first before the second. Scrape bowl and paddle as needed.
Continue on medium until homogeneous, about 30 seconds after the second egg.
Finish dough
Reduce speed to low; add reserved sifted flour mixture and chocolate.
Mix until homogeneous with no visible dry flour, about 1 minute.
Stop and detach bowl.
Portion and rest
Line a half sheet pan with parchment.
Using a #10 scoop, divide dough into 16 portions (~100 g each).
Roll into smooth balls; return to pan.
Wrap tightly and refrigerate until fully chilled, at least 2 hours and up to 12 hours (ideal 4 hours).
May refrigerate up to 1 week or freeze up to 6 months in freezer bags.
Bake and shape
Preheat oven to 350 °F / 177 °C (convection fan on) or 375 °F / 191 °C (conventional).
Space chilled portions 3 inches apart on parchment-lined half sheet pans, max 6 per pan (3 pans for all 16).
Bake one sheet at a time.
Optional: sprinkle flake sea salt as hot cookies exit the oven.
Bake until edges are set and centers still soft; cool on pan briefly, then on a rack.