Preheat oven to 350 degrees F. Line 2 baking sheets with parchment or silicone liners; set aside.

In a large bowl of a stand mixer, cream together the butter, brown sugar, and granulated sugar until creamy and blended, about 1 minute. Add in the eggs, one at a time, followed by the vanilla. Lastly, add in the baking soda, salt, flour, and pudding powder until a soft dough comes together. Stir in the white chips, cookies, and sprinkles.

Drop 1-2 Tablespoonfuls of dough 2" apart on the baking sheet. Bake for 10-12 minutes, rotating pans halfway through baking time to ensure even cooking. Let cool out of the oven for about 5 minutes before pressing a whole circus animal cookie into the center of each cookie. Allow cookies to cool completely before serving or storing.