Place the cold, cubed butter and granulated sugar into the bowl of a stand mixer fitted with the paddle attachment. Mix on low speed for 30 seconds, then increase to medium speed for another 30 seconds. Finish on high speed for 30 seconds until the mixture looks light, fluffy, and slightly pale. Using cold butter helps create a thick, bakery-style cookie.

Beat in the eggs one at a time, mixing well after each addition. Add the vanilla extract and mix just until combined. The mixture should be smooth and creamy.

Add the cornstarch, baking soda, salt, cake flour, and all-purpose flour. Mix on low speed until no dry pockets remain. Stop mixing as soon as the dough comes together to prevent a dense texture.

Gently stir in the chopped frosted circus animal cookies, white chocolate chips, and rainbow sprinkles. The dough should be thick, colorful, and studded with visible pieces.

Cover the bowl and refrigerate the dough for 20 minutes. This short chill firms the butter and helps the cookies keep their shape while baking.

Preheat the oven to 400°F and line one baking sheet with parchment paper. Using a digital scale, portion 6 ounces of dough per cookie and shape into loosely packed, tall balls. Place only four dough balls on the sheet, spacing them about 3 inches apart.

Bake on the center rack, one sheet at a time, for 10 to 13 minutes. The cookies are ready when the outside looks dull and lightly golden, while the centers remain soft and slightly underbaked. Baking one test cookie can help determine the ideal timing for your oven.

Remove the cookies from the oven and let them cool on the baking sheet for up to 30 minutes. They will be delicate at first and continue to set as they cool. Keep the remaining dough refrigerated between batches.