In a medium saucepan, combine heavy cream, whole milk, and granulated sugar. Heat over medium heat, stirring frequently for about 5–7 minutes until the sugar fully dissolves. Remove from heat and stir in the vanilla extract. Pour the base into a bowl, cover, and chill in the fridge for at least 2 hours until completely cool.

Prepare the raspberry layer by blending fresh raspberries with 2 tablespoons of sugar until smooth. Strain the mixture using a fine mesh sieve to remove the seeds.

Once the cream base has chilled, pour it into your ice cream maker and churn according to the manufacturer’s instructions until it reaches a soft-serve consistency, about 20–25 minutes.

Divide the churned cream base into three equal portions in separate bowls. Mix the raspberry puree into one bowl, orange juice and zest into another, leaving the last portion plain.

Churn each flavored portion in the ice cream maker separately for an additional 10–15 minutes until each reaches a soft-serve texture.

In a freezer-safe container, layer spoonfuls of each flavored mixture alternately—raspberry, orange, and lime. Use a spatula to gently swirl for a marbled effect.

Cover the container and place it in the freezer. Allow the sherbet to freeze for at least 4–6 hours until firm enough to scoop.