In a medium saucepan, combine the heavy cream, milk, and granulated sugar over medium heat. Stir continuously for about 5 to 7 minutes until the sugar fully dissolves and the mixture begins to steam, but do not let it boil.

Once done, remove from heat, stir in the vanilla extract, and let the mixture cool completely.

While the base is cooling, add fresh or thawed raspberries and a tablespoon of sugar to a blender. Blend until smooth, then strain the mixture through a fine mesh sieve to remove the seeds.

Once the cream base has cooled, place it in the refrigerator and chill for at least 2 hours until it's very cold.

After chilling, pour the base mixture into your ice cream maker. Churn according to the manufacturer’s instructions until it reaches a soft-serve consistency, typically around 20-30 minutes.

Divide the churned base into three equal parts. In a separate bowl, mix one part with freshly squeezed orange juice and a drop of orange food coloring. Gently fold until well combined.

Next, take another part of the base and mix it with freshly squeezed lime juice and a few drops of green food coloring.

Now, pour the final third of the base into a bowl and stir in the raspberry puree, mixing well.

Grab a freezer-safe container and start layering the three sherbet flavors, alternating spoonfuls of the orange, lime, and raspberry mixtures.

Cover the container tightly and place it in the freezer. Let it freeze for at least 4 to 6 hours, or until it becomes firmer and scoopable.

Once your Homemade Rainbow Sherbet is set, scoop it into colorful cones or bowls.