In a blender or food processor, purée the cantaloupe. Strain through a fine mesh sieve. (No need to strain if puréed smooth). In a large saucepan over medium heat, add the puréed cantaloupe, heavy cream, and half-and-half. Cook until warm but do not let it come to a boil.
In a medium bowl, stir together the eggs, sugar, vanilla, lime juice, ginger, and salt. Stir ½ cup of the warm cream mixture to the egg mixture, then whisk into the saucepan. Over medium-low heat, bring the cantaloupe-cream mixture to a simmer, stirring occasionally, for about 8 minutes or until the mixture gets slightly thick.
Transfer into medium-size bowl, cover in plastic wrap, and cool in the refrigerator for 4 hours. Pour into an ice cream machine and churn according to your ice cream maker's instructions. Serve and/or transfer to a 1-quart freezer proof or a 9 x 5-inch loaf pan and freeze.