Step 1: Preheat your oven to 375°F (190°C). Line two baking sheets with parchment paper or silicone mats.
Step 2: In a medium bowl, whisk together the all-purpose flour, cornstarch, baking powder, baking soda, and salt. Set aside.
Step 3: In a large bowl, using an electric mixer, cream together the softened unsalted butter, granulated sugar, and light brown sugar until light and fluffy, about 2-3 minutes.
Step 4: Beat in the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
Step 5: Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Do not overmix. Stir in the semi-sweet and milk chocolate chips.
Step 6: Divide the cookie dough roughly in half. To one half, add the unsweetened cocoa powder and mix until just incorporated and uniformly chocolate-colored. Leave the other half as vanilla dough.
Step 7: To create the marble effect, take small, irregular pieces of both vanilla and chocolate dough (about 1 tablespoon each) and gently press them together. Lightly twist or fold them once or twice to create swirls, then form into a ball. Place the swirled dough balls onto the prepared baking sheets, about 2 inches apart.
Step 8: Bake for 10-12 minutes, or until the edges are lightly golden and the centers are still slightly soft. Let the cookies cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.