Preheat the oven to 350 degrees.
Lightly grease a cookie sheet or line with parchment paper, set aside.
Using a hand mixer or a stand mixer fitted with the paddle attachment, cream the butter and sugar until smooth.
Add in eggs and vanilla extract, beat until combined. Scrape down the bowl once complete.
In a separate bowl, whisk together dry ingredients (flour, pudding mix, salt, baking soda).
Add dry ingredients to wet ingredients in 2-3 portions, mixing well after each addition.
Coarsely crush the frosted animal crackers by placing them in a gallon bag and rolling them with a rolling pin (or coarsely chop them with a knife). Reserve some for topping the cookies after baking. Add them to the dough and mix until combined.
Use a wooden spoon or rubber spatula to fold the sprinkles and white chocolate chips into the dough (reserve some white chocolate chips for topping the cookies after baking).
Use a spoon or cookie dough scoop to measure and ball the cookie dough (if you are not using a cookie dough scoop, you should roll the dough into balls with your hands).
Place balled cookie dough on to prepared cookie sheet, leaving at least 1 inch in between each cookie.
Bake for 10-12 minutes or until the bottom just begins to brown (cookie edges should just barely brown before removing from the oven).
Immediately upon removing them from the oven, swirl with a cookie cutter or water glass that is slightly larger than the baked cookie. Then top with additional frosted animal crackers and white chocolate chips if desired.
Let the cookies rest for 5-10 minutes, then move them to a cooling rack and cool to room temperature. Then enjoy!