Wash and drain mint leaves. Bruise the leaves using so that they soften and release some of their oil. Set aside.
Combine 2 cups of whole milk, heavy cream, and sugar in a medium saucepan. Heat over medium/high heat, stirring to dissolve the sugar. Bring to a boil, then remove from heat. Add the mint leaves to the warm milk. Cover and let steep for 25 minutes, then strain out the leaves.
In a small glass, combine 2 tablespoons of milk and the cornstarch. Stir vigorously to create a slurry, then stir slurry into the mint-milk mixture.
Return saucepan to the heat and bring to a boil. Let boil for 1 minute, stirring frequently, until it begins to thicken. Remove from heat.
Stir together the cream cheese and a pinch of salt in a large bowl. Add the hot milk mixture and whisk until fully combined. Cover and chill in the refrigerator until cool.
While the base is chilling, chop the chocolate bar into small pieces. Place chocolate chunks in a plastic bag and chill in the freezer until ready to use.
When base is completely cool add it to an ice cream maker and process according to the manufacturer’s instructions. Stir in the chilled chocolate pieces. Transfer to an airtight container and freeze for at least 2 hours before serving.