Mix Dry Ingredients: In a medium bowl, sift together the bread flour, cake flour, baking soda, baking powder, and salt. Set aside.

Cream Butter and Sugars: In a stand mixer fitted with a paddle attachment, cream the butter and sugars together until very light and fluffy, about 5 minutes. Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.

Combine Wet and Dry Ingredients: Reduce the mixer speed to low, then slowly add the dry ingredients and mix until just combined (5 to 10 seconds). Drop in the chocolate pieces and incorporate them without breaking them.

Chill the Dough: Press plastic wrap against the dough and refrigerate for 24 to 72 hours. The longer the dough rests, the better the cookies will be.

Bake: When ready to bake, preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper or a nonstick baking mat. Scoop 6 3 1/2-ounce mounds of dough (the size of generous golf balls) onto the baking sheet, making sure to space them evenly. Bake for 18 to 20 minutes, until golden brown but still soft. Let the cookies cool on the sheet for 10 minutes before transferring them to a wire rack to cool completely.