Cut a thin layer off top of chocolate genoise to make a flat surface and sprinkle with 1/4 cup brandy. Place on a plate.
Melt 6 ounces chocolate: put chocolate in bowl and cover with hot water. Let stand until chocolate is soft, then pour off water, leaving softened chocolate behind. Add chocolate to whipped cream and beat together. Add 1/4 cup rum.
Spread layer of creamed chocolate over chocolate layer of genoise and top with yellow genoise. Sprinkle remaining 1/4 cup rum over top layer.
Beat egg whites until stiff. Cream together butter and sugar until light and fluffy. Add egg whites, a little at a time, until incorporated. Spread all but 1/2 cup buttercream over top of cake and dust with icing sugar. Place another layer of ganache on top and spread smoothly. Arrange apricots around top of cake.
Melt remaining chocolate in bowl, as before and pour over top of cake. Decorate with pipings of reserved buttercream.
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