This is a case of "if ain't broke, don't fix it" meaning we could reinvent yet another classic chocolate ice cream but it's hard to get better than this version by Jeni's Splendid Ice Cream. Made by mixing a rich coffee-chocolate sauce into a vanilla base it's our go to for homemade ice cream and was the master recipe for our chocoalte ice creams at our Ice Cream Social!
Make the ice cream: In a bowl, stir together 1/4 cup milk and the cornstarch; set slurry aside. In a 4-quart saucepan, whisk together remaining milk and the cream, 1/2 cup of the sugar, syrup, and salt; bring to a boil over medium-high heat. Cook for 4 minutes; stir in slurry. Return to a boil and cook, stirring, until thickened, about 2 minutes. Place cream cheese in a bowl and pour in 1/4 cup hot milk mixture; whisk until smooth. Then whisk in remaining milk mixture.
Make the chocolate sauce: Bring cocoa, brewed coffee, and remaining 1/2 cup sugar to a boil in a 2-quart saucepan over high heat; cook for 30 seconds. Remove from heat and stir in chocolate.