Cut cold butter into cubes. In a stand mixer with a whisk attachment, or a large bowl with a hand mixer, cream together butter and brown sugar for 3–4 minutes until the consistency is similar to peanut butter.
Beat in eggs and vanilla. Add the cornstarch, baking soda, salt, and cocoa powder and mix until just combined. Mix in the cake flour and all-purpose flour until no streaks remain. Avoid overmixing. Fold in the chocolate chips, then tightly cover and refrigerate the dough for at least 30 minutes up to an hour.
If the dough chilled longer than an hour, let it soften slightly at room temperature. Preheat the oven to 350°F. Roll the dough into 2-tablespoon sized balls (40 grams each). Place powdered sugar in a bowl and roll each dough ball generously to coat.
Space the cookies 2 inches apart on a lined sheet pan. Bake for 8-12 minutes, leaning toward the shorter bake time for fudgier cookies. Once out of the oven, gently press any uneven edges inward with a spatula. Let the cookies rest on the pan for 5 minutes, then use a spatula to move them to a cooling rack.
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Notes
Note 1: Use Dutch-process cocoa for the best flavor and texture. Regular cocoa makes the cookies drier and less flavorful. Spoon and level the cocoa to avoid adding too much.Note 2:Cake flour is essential for a soft, tender texture. Don’t substitute or use DIY cake flour here.Note 3: I love milk chocolate, but semi-sweet, white, or dark chocolate also work great.Note 4: If cookies haven’t spread by 7 to 8 minutes, briefly remove the pan and tap it on the counter 2 to 3 times. Return the pan to finish baking.Storage: Store cookies in an airtight container at room temperature for up to 1 week. Warm leftovers in the microwave. Dough balls can be frozen and baked straight from frozen with a few extra minutes added.