Butter the bottom and sides of a 9-inch springform pan.
Dust the inside of the pan with the cocoa powder and tap out the excess.
Wrap the outside of the pan with the heavy-duty aluminum foil.
Melt the chocolate and the butter together in a large bowl over simmering water until smooth.
Remove from the heat and let cool slightly.
Whip the eggs and the sugar on high speed for 4-5 minutes until pale, thick, and tripled in volume.
Stream the cooled chocolate mixture into the egg mixture on low speed.
Add the rum, the vanilla, and the salt, mixing just until combined.
Pour the batter into the prepared pan and smooth the top.
Bake for 30-35 minutes until edges are set but center jiggles slightly.
Let the cake cool completely in the pan on a wire rack.
Run a thin knife around the edge and release the springform pan.
Dust with the cocoa powder before serving.