Combine the lime juice, chopped mint leaves, and cantaloupe in a food processor or blender until smooth.
Add the purée, a large handful of whole mint leaves, and ¼ cup of sugar to a small saucepan and cook over medium heat, stirring, until the sugar dissolves, but do not boil. Transfer to a bowl and let cool.
Ice cream base
Whisk the corn starch in a small bowl with about 3 tablespoons of the milk to make smooth slurry. Set aside.
In a large bowl, whisk the cream cheese with about 1 tablespoon of the milk until smooth.
Prepare an ice bath by filling a large bowl with ice cubes and water.
In a medium saucepan, combine the remaining milk, cream, sugar, and corn syrup, and bring it to a boil over medium-high heat. Let it boil for 4 minutes. Remove from heat.
Give the corn starch slurry one last whisk to make sure it's completely incorporated. Slowly whisk the corn starch slurry into the hot milk saucepan and return it to medium-high heat.
Bring it back to boil and cook, stirring, until it lightly coats the back of a wooden spoon, about 1-2 minutes. Remove from heat.
Slowly pour the hot milk into the cream cheese bowl and mix until smooth.
Slowly pour in the cantaloupe mixture and whisk until smooth.
Pour the mixture into a large 1-gallon Ziploc bag. Seal it and submerge the mixture in the ice bath until cold, about 30 minutes.
Pour your ice cream base into your frozen ice cream maker bowl. Follow the directions on your ice cream maker to mix the batter into ice cream, until thick and creamy.
Pack the ice cream into an air-tight storage container, pressing a sheet of parchment paper directly against the ice cream.
Freeze until firm, at least 4 hours, but preferably overnight.
This nutritional information has been automatically calculated, and as such, may be incomplete or inaccurate. Please reference the specific ingredients you use for the most accurate nutritional information.