Whisk to combine the flour, baking soda, baking powder, and cornstarch in a large bowl; set aside. Beat the butter and both sugars on medium-high speed in the bowl of a stand mixer fitted with a paddle attachment (or in a large bowl if using a handheld mixer) until light and fluffy, about 4 minutes. Add the eggs, one at a time, beating after each addition to incorporate.

Transfer the cookie dough into a medium bowl, cover it tightly, and chill in the refrigerator for at least 30 minutes. If chilling for 3+ hours, make sure you let the cookie dough sit at room temperature for at least 1o to 15 minutes before rolling into balls; the cookie dough will be very stiff after being in the fridge that long.

Using a 2-inch ice cream scooper, scoop the dough, scraping each against the bowl as you scoop. Roll each mound in your hands to form a ball.

Place on the prepared baking sheet, about 2 to 3 inches apart. Bake one sheet at a time until the cookies have puffed up and the tops begin to crackle, 10 to 11 minutes; do not overbake.

Remove from the oven and let cool slightly on the baking sheet, then transfer the cookies to a wire rack to cool completely. Repeat forming the remaining dough into balls. Store the walnut chocolate chip cookies in an airtight container.