In a medium saucepan, combine 2 cups of heavy cream, 1 cup of whole milk, and 1 cup of granulated sugar. Heat over medium heat, stirring gently for 5-7 minutes until the sugar dissolves and mixture is warm but not boiling. Remove from heat and stir in 1 tablespoon of vanilla extract. Allow to cool completely for approximately 30 minutes.

While the base cools, prepare the raspberry flavor layer. In a blender, combine 2 cups of fresh raspberries with 1/4 cup of granulated sugar. Blend until smooth, then strain through a fine mesh sieve to remove seeds, resulting in a silky raspberry puree. Set aside.

Once the base is cooled, pour it into your ice cream maker. Churn according to manufacturer's directions for about 20-25 minutes until it reaches a soft-serve consistency.

Divide the churned base into three bowls. For the orange layer, mix in 1 cup of fresh orange juice, zest from one orange, and a few drops of green food coloring into one bowl. For another bowl, blend in 1/4 cup of lime juice and optional lime zest. Fold the raspberry puree into the last portion of the base.

In a large, airtight container, layer the sherbet flavors, starting with raspberry, followed by the orange layer, and then the lime layer, gently swirling together with a spatula. Cover and freeze for 4-6 hours or until solid.