Heat the oven to 350°F and line a cookie sheet with parchment or a silicone baking mat.
Whisk the flour, cornstarch, baking soda, and salt together in a bowl.
Beat the butter, brown sugar, and granulated sugar on medium speed for 2 minutes, until fluffy and pale.
Beat in the eggs and vanilla for 30 seconds.
Gradually mix in the dry ingredients on low speed. Add the blue and violet gel colors before the dough is fully mixed, then continue until thick and evenly colored.
Stir in one-third of the white chocolate chips, chopped Chips Ahoy cookies, and chopped Oreos by hand.
Scoop 2-tablespoon portions, roll smooth, press the remaining mix-ins onto the outside, and arrange about eight per sheet. Bake one sheet at a time for 10 to 12 minutes, removing before the edges brown.
Cool the cookies on the baking sheet for 15 minutes before moving them.