In a medium saucepan, combine cream, milk, and sugar over medium heat. Stir until sugar dissolves for about 5–7 minutes. Remove from heat and stir in vanilla extract, then allow to cool completely.

Wash raspberries and add them to a blender with a bit of sugar. Blend until smooth, strain through a fine mesh sieve for raspberry puree. Set aside.

Transfer cooled base to an airtight container and refrigerate for at least 2 hours.

Pour the cold base mixture into an ice cream maker and churn for about 20–25 minutes until soft-serve consistency.

Divide churned base into three parts. To one part, add orange juice and optional zest, then churn for about 5 minutes.

To the second part, mix lime juice and optional zest, then churn again for 5 minutes.

To the final part, stir in the raspberry puree and churn for another 5 minutes.

In a freezer-safe container, layer the orange, lime, and raspberry mixtures, smoothing the top. Cover tightly and freeze for 4–6 hours.

Once frozen, scoop sherbet into bowls or cones and enjoy.