Sift 2 cups minus 2 tablespoons cake flour, 1¾ cups bread flour, 1⅛ teaspoons salt, 1½ teaspoons baking powder, and 1¼ teaspoons baking soda into a large bowl. Set aside.
In a stand mixer fitted with a paddle attachment, cream together the 1¼ cups unsalted butter, 1¼ cups light brown sugar, and 1 cup + 2 tablespoons granulated sugar on speed 4 until very pale and light, about 5 minutes. I scraped down the bowl and the paddle halfway through, even though it does not say to do so in the original recipe.
Add 2 large eggs, one at a time, mixing for 30 seconds on speed 2 after each addition. Stir in the 2 teaspoons pure vanilla extract.
Add about half of the dry ingredients and mix on low, then add the other half while it mixes and mix for another 5 to 10 seconds until just combined.
Chop the 1¼ pounds bittersweet chocolate Ghirardelli Bars into squares (each of the molded chocolate squares becomes 4 squares).
Add the squares and any smaller pieces to the bowl and fold it into the dough without breaking it (as much as possible).
Portion the dough into 3½-ounce mounds of dough and place them close together on a large parchment-lined baking pan. Flatten out any chocolate pieces that are poking up; it will make for a more attractive cookie. Top with a few chunks of extra chocolate for appearances and pools of chocolate on top of the baked cookie if any are looking sparse.
Cover with plastic wrap and chill in the refrigerator for 24 to 72 hours. (the longer, the better). The dough can be used all at once or in batches.
Preheat the oven to 350°F and line two large baking pans with parchment paper. Chill one for 2 minutes in the freezer before adding cookies. Set the other aside for the second batch, chilling it for a few minutes before you put the cookies on to bake. Only bake one baking pan worth of cookies at a time for best results.
Bake no more than six cookies per 12x17-inch baking pan, leaving 3 inches between cookies, until golden brown but still soft, about 18 to 20 minutes for large cookies or 10 to 12 minutes for smaller cookies. Rotate halfway through.
Sprinkle lightly with Flaky sea salt right after they come out of the oven.
Transfer the baking pan to a wire rack for 10 minutes, then transfer the cookies from the pan to another wire rack to cool further. Place the used baking sheet in the freezer to chill for a few minutes before adding the next batch to it. They are best eaten warm.
Optional: For the signature chocolate bottom, melt dark chocolate melting wafers in a microwave-safe bowl at 30-second intervals, stirring between each one, until entirely melted. Gently dip the bottoms of the cooked and firm cookies in the chocolate and place them on parchment paper to set.