Place chocolate in a medium metal or glass 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 saucepan over medium heat until mixture begins to boil; set aside.
In a stand mixer, beat egg yolks and 7 Tbsp (90 g) sugar 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 temperature reaches 175°F (80ºC), 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 the remaining 6 Tbsp (80 g) sugar and 2 Tbsp water to a boil in a small saucepan over medium-high heat, stirring until sugar dissolves.
Boil, occasionally swirling the pan (do not stir), until 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.
Notes
If you don't have an ice cream maker, check out here.Barely adapted from Bonappetit. The original recipe recommends you make it at least 3 days ahead.