Sift Flour & Cream Butter + Sugar. In a large bowl, sift together cake flour, bread flour, baking soda, baking powder, and salt. In a separate bowl, combine the room-temperature butter, granulated sugar, and light brown sugar. Using an electric mixer, cream the butter and sugars for about 5 minutes, until light and fluffy.
Add Eggs & Vanilla. Add the eggs one at a time, mixing well after each addition. Add the vanilla extract and mix until fully incorporated.
Chop Chocolate. Roughly chop the Valrhona dark chocolate fèves into large chunks (about four pieces per fève). Set aside.
Add Dry Ingredients & Chocolate. Add the sifted flour mixture to the dough in two batches, gently mixing until just combined. Do not overmix. Add the chopped chocolate.
Fold Chocolate into Dough. Using a spatula, gently fold the chocolate into the cookie dough, being careful not to break the chocolate pieces.
Wrap & Refrigerate Dough. Divide the cookie dough into three portions and place each portion on plastic wrap. Shape into logs, wrap tightly, and refrigerate for 72 hours (or less if needed).
Bake Cookies. Preheat the oven to 350°F. Weigh out 3½ ounces of cookie dough and roll into a ball. Place on a greased baking sheet, flatten slightly, and sprinkle with flaky sea salt. Bake for 18–20 minutes, until golden brown. Enjoy warm.