Place chocolate in a medium metal bowl. Set bowl over a saucepan of barely simmering water. Stir chocolate until melted and smooth. Set melted chocolate aside; let cool slightly.

Whisk milk and cocoa powder in a medium heavy saucepan over medium heat until mixture begins to boil; set aside.

Using an electric mixer, beat egg yolks and 7 tablespoons sugar in another medium bowl until very thick ribbons form, about 2 minutes. Whisking constantly, gradually add hot milk mixture to egg yolk mixture. Return mixture to saucepan. Add melted chocolate and whisk to blend. Stir over low heat until slightly thickened and an instant-read thermometer registers 175°, about 5 minutes. Transfer chocolate custard to a large bowl and place over another large bowl of ice water. Stir until chocolate custard is cool.

Bring remaining 6 tablespoons sugar and 2 tablespoons water to a boil in a small heavy, deep saucepan over medium-high heat, stirring until sugar dissolves. Boil, occasionally swirling pan and brushing down sides with a wet pastry brush (do not stir), until a dark amber color forms, about 5 minutes. Gradually whisk in cream (mixture will bubble vigorously). Whisk caramel into chocolate custard. Strain into a large container; cover and chill for 2 days.

Process custard in an ice cream machine according to manufacturer's instructions. Transfer to another container; freeze for 3 days before eating.