Stir together milk, chocolate, and 1 teaspoon vanilla in a medium saucepan over low heat. Cook, stirring constantly, 8 minutes or until mixture begins to bubble around edges and chocolate is melted and smooth. Stir in coffee. Remove from heat; set aside.
Beat cream, sugar, and remaining 1/2 teaspoon vanilla at high speed with an electric mixer until soft peaks form.
Pour hot coffee into mugs. Top with whipped cream.