To make the ice cream base, combine the milk and cream into a medium bowl. Whisk in the sugar and the California Olive Ranch extra virgin olive oil. Continue to whisk vigorously for about 30 seconds to dissolve the sugar.
Pour the ice cream base into a counter-top ice cream maker. Following the manufacturers instructions for your appliance, freeze for about 20 minutes.
Stir the salt into the honeydew melon puree and slowly pour the puree into the ice cream maker as it churns. Let it continue to churn for about 10 more minutes, or until the ice cream becomes firm.
It can be eaten right away as a softer ice cream, or transfer it to a freezer-safe container and freeze for 4 hours, until firm. Scoop and serve.