In a medium saucepan, heat 2 cups of heavy cream, 1 cup of whole milk, and 2 tablespoons of smashed fresh ginger over medium heat. Stir occasionally until the mixture is just scalding, which takes about 5-7 minutes.

In a mixing bowl, vigorously whisk together 4 egg yolks and 3/4 cup of sugar until thick and pale, about 2-3 minutes.

Gradually pour the hot cream mixture into the egg and sugar mixture while continuously whisking to temper the eggs. Return the combined mixture to low heat, stirring until thickened, about 5-7 minutes.

Remove from heat, stir in 1 teaspoon of vanilla extract, and strain through a fine-mesh sieve into a bowl. Set in an ice bath for 20-30 minutes, then refrigerate for 4-6 hours.

In a blender, puree 2 cups of diced cantaloupe with 1/2 cup of milk until smooth. Strain the puree to remove pulp, then stir in 1/4 teaspoon of sea salt.

Pour the cooled ice cream base into an ice cream maker and churn for about 15 minutes. Add the cantaloupe mixture in the last 5 minutes.

Serve immediately as soft-serve or transfer to a container, press with parchment, and freeze for at least 4 hours until firm.