Mix together all ingredients except for cookies and sprinkles and pour into 2 qt. ice cream maker.
Follow manufacturer's directions.
When ice cream is almost completely set up, add in cookies and sprinkles and process enough to get them incorporated.
Place ice cream in freezer to firm up.
Notes
Break the cookies into bite-sized pieces. A mix of larger chunks and smaller pieces gives you the perfect cookie-to-ice cream ratio in every bite.
Add the cookies at the end. Fold the circus animal cookies into the ice cream during the last few minutes of churning or by hand after churning. This helps them keep a little crunch instead of becoming too soft.
Use jimmies instead of nonpareils. Long rainbow sprinkles (jimmies) hold their color much better than tiny round nonpareils, which can bleed into the ice cream and create streaks of color.
Don't overmix the sprinkles. Gently fold them in at the end to keep the colors bright and distinct.
Freeze before serving. Freshly churned ice cream has a soft-serve consistency. For firmer, scoopable ice cream, transfer it to a freezer-safe container and freeze for 2–4 hours before serving.
Let it soften before scooping. If the ice cream has been in the freezer overnight, let it sit on the counter for 5–10 minutes for easier scooping.
Have fun with toppings. For an extra festive treat, top each scoop with additional crushed circus animal cookies, rainbow sprinkles, whipped cream, or even a maraschino cherry. It's the perfect finishing touch for birthdays or celebrations.