Ideally the night before: place the aquafaba in a small pan over high heat and let it boil, uncovered, until reduced by about half (to 1.5 oz or about 3 tablespoons). Set aside and refrigerate for at least four hours or overnight.
To make the cake, preheat oven to 350 degrees. Melt together the butter and chocolate in a microwave safe container for 30 seconds. Stir and microwave for another 30 seconds. Stir until the mixture is smooth and set aside to cool. Use this time to prep your loaf pan: line it with parchment paper and grease well.
Meanwhile, whip the eggs on high speed until doubled in size, about 5 minutes. Once chocolate mixture has cooled a bit, fold in a third of the whipped eggs. Fold the rest of the eggs in a third at a time until mixture is homogenous and light.
Pour mixture into your prepared pan and bake for 20 minutes, or until top is matte and cake is set, but still soft.
Remove the cake from the pan and let cool in the parchment on a rack until room temperature (at least 30 minutes), then refrigerate if time permits.
While cake is cooling, add the chilled aquafaba, cream of tartar, and vanilla to a stand mixer with a whisk attachment. Whip on high until very foamy and approaching soft peaks. Add sugar one tablespoon at a time until aquafaba turns glossy, voluminous and soft peaks. Fold in the cocoa powder with a spatula until you reach desired marbled effect.
Preheat the broiler to 475 degrees F. Make sure the cake is no longer hot (to prevent melting the aquafaba). Dollop the meringue over the top. Broil for 1-2 minutes, until it starts to turn golden on top. Meringue will feel slightly dry to the touch where torched by the broiler.
Serve at room temperature or chilled. Store in the fridge. Meringue may deflate slightly in the fridge, but still hold up for at least a few days!