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Step 1
Heat the oven to 325°F with a rack in the middle position. Coat the bottom and sides of a 9-inch springform pan evenly with the tablespoon of softened butter. In a 2-cup liquid measuring cup, combine the prunes, rum and molasses. Microwave until the rum is bubbling, 45 to 60 seconds. Let sit for 15 minutes, stirring occasionally.
Step 2
In a medium saucepan over medium heat, melt the remaining 8 tablespoons of butter.Remove from the heat and immediately add the chocolate, then whisk until melted and completely smooth.In a large bowl, whisk together the egg yolks and 71 grams (⅓ cup) of sugar until pale and glossy, about 30 seconds.Slowly add the melted chocolate mixture and continue whisking until smooth. Stir in the prune mixture.
Step 3
Using a stand mixer with a whisk attachment, whip the egg whites and salt on medium-high speed until light and foamy, about 1 minute. With the mixer running, slowly sprinkle in the remaining 54 grams (¼ cup) of sugar and continue to whip until the whites are thick and glossy and hold soft peaks, about 1 minute.
Step 4
Whisk ⅓ of the whipped egg whites into the chocolate mixture to lighten it.Gently fold in the remaining whites with a rubber spatula until the batter is marbled but not fully blended.
Step 5
Pour the batter into the prepared pan. If needed, smooth the top with a spatula. Bake until the edges of the cake are firm and cracked, 35 to 40 minutes. The center will be just set, yet soft to the touch.Cool the cake in the pan on a wire rack for at least 1 hour before serving (the cake will settle and sink as it cools).