To start making Bruster's Birthday Cake ice cream, you need to prepare the ice cream base. In a large bowl, whisk together the heavy cream, whole milk, and granulated sugar until the sugar has dissolved. Add the cake mix and whisk until the mixture is smooth and well combined.

Next, add the rainbow sprinkles to the ice cream base and stir until they are evenly distributed throughout the mixture. The sprinkles will give the ice cream its signature fun and festive appearance.

Add the vanilla extract to the ice cream base and stir until it is well incorporated. The vanilla extract will give the ice cream a rich and creamy flavor that complements the cake batter and sprinkles.

Place the ice cream base in the refrigerator and chill it for at least 2 hours or until it is completely chilled. Chilling the mixture will help it thicken and develop a smooth and creamy texture.

Once the ice cream base is chilled, it's time to churn it into ice cream. Pour the mixture into an ice cream maker and churn it according to the manufacturer's instructions. This will typically take between 20-30 minutes.

In the last few minutes of churning, add the chopped cake pieces to the ice cream and continue churning until the cake is well distributed throughout the ice cream.

Once the ice cream has been churned, transfer it to a container with a tight-fitting lid and freeze it for at least 2 hours or until it is completely frozen. This will allow the ice cream to harden and set, so it has a firm texture that is easy to scoop.