In a small bowl, combine 2 Tablespoons milk with cornstarch, whisk and set aside. Combine remaining milk, ½ cup (118ml) cream, salt, and 1/3 cup (67g) sugar in a medium saucepan and place over medium heat. Bring milk mixture to a low boil. Cook until the sugar dissolves, 3 minutes.
Remove milk mixture from heat and gradually whisk in the cornstarch mixture. Return to a boil and cook over moderately high heat until the mixture is slightly thickened, about 1 minute. Pour base into the chocolate liquor and whisk to combine. Stir in remaining 1 cup (237ml) cream. Set bowl in the ice water bath to cool, 20 minutes, whisking occasionally. Once cool, add vanilla. Refrigerate ice cream base until chilled, at least 4 hours or overnight.