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To make the filling: In a large bowl or the bowl of a stand mixer, beat all the ingredients until smooth. Set aside 2 tablespoons (about 25g) of the filling in a small bowl; you will use this for the icing.
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To assemble the cake: Using a large serrated knife, cut the cake in half horizontally to create 2 layers. Place the top layer, cut side up, on a serving plate. Dollop the filling over it and spread evenly with a small offset spatula, leaving a 1/2" border around the edges.
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Place the bottom layer, cut-side down, on top of the first (the bottom of the baked cake will now be on the top) and gently press to adhere, smushing the filling all the way to the edges. Set aside while you prepare the ganache.
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To make the ganache: In a microwave-safe bowl or measuring cup, combine the cream and chocolate and heat in 20-second increments, at 50% power, stirring after each, until smooth. Chill in the refrigerator, uncovered, for 10 to 15 minutes, until the ganache is the consistency of molasses. (Partially cooling will help the ganache coat the top of the cake without dripping down the sides.)
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To make the icing: Add the cream, 1/2 teaspoon at a time, to the reserved filling, mixing with a spatula until thoroughly combined. Aim for a consistency that’s thin enough to pipe but thick enough to hold its shape. Transfer the icing to a parchment cornet or plastic bag.
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Once the ganache has cooled, pour it over the center of the cake and use a small offset spatula to spread it just to the edges. Be sure to spread the ganache slowly to prevent it from dripping down the sides of the cake.
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Cut the tip off the cornet (or cut a corner off the plastic bag) to make a small hole, then pipe a single looped line of icing across the top of the cake. (For the cleanest slices, wait for the ganache to set, about 2 hours; you can speed up the process by transferring the cake to the refrigerator to set.)
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Storage information: Store the cake, covered, at room temperature for up to 4 days; freezing is not recommended.