Freeze your ice cream maker bowl according to the manufacturer’s instructions. In a large bowl, whisk together the whole milk, heavy cream, granulated sugar, cake batter flavor, and vanilla extract until the sugar is dissolved. Make sure the sugar is fully dissolved, otherwise your ice cream will have a gritty texture. If you’re having trouble dissolving the sugar, blend the mixture on high speed in a blender for 30 seconds. Transfer the mixture to your ice cream maker and churn according to the manufacturer's instructions until it reaches a soft-serve consistency. Depending on your ice cream maker, this should take 15-25 minutes. Place the frosting in a small bowl and heat in the microwave for 5-10 seconds, or until it is just barely pourable. Add a drop of blue food coloring to the frosting and stir to combine. Add more if desired. When the ice cream is done churning, transfer ⅓ of it to a 9" x 5" loaf pan and drizzle the blue frosting over the ice cream. Use a butter knife to swirl the frosting into the ice cream. Top with rainbow sprinkles. Repeat with the remaining ice cream, frosting, and sprinkles two more times – creating another two layers, ending with frosting and sprinkles on top for garnish. Cover the loaf pan tightly with plastic wrap and freeze for at least 6 hours, or until the ice cream is fully set. Then scoop and enjoy.