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For the cake:
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Preheat oven to 350 degrees, then butter and flour an 8-inch square pan.
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Melt the butter, pour into a large bowl and allow it to cool slightly. Beat the sugar and eggs into the butter.
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In a separate medium bowl, whisk together the flour, cinnamon, cloves, dry baking soda and grated ginger.
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Bring 1 cup of water to a boil in a small saucepan. Using a wooden spoon, stir the molasses and the baking-soda solution into this water.
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Whisk the dry ingredients into the sugar and eggs, then stir in the molasses mixture.
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Pour the batter into a prepared pan and bake until a toothpick inserted in the center of the cake pulls out cleanly, about 40 minutes to 1 hour.
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Cool cake on a wire rack for 10 minutes. Run a knife around the rim of the pan to loosen the cake and invert onto a cooling rack to cool completely.
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For the lime cream:
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Whip the eggs and sugar in a bowl of an electric mixer, using the whisk attachment until the mixture doubles in volume and has a light color. Lower the speed and blend in the lime juice and zest.
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Pour this mixture in the top of a double boiler (or into a medium metal bowl placed over a pot of simmering water). Cook over high heat, whisking often until smooth , very thick and custard-like.
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Remove from the heat and use a wooden spoon to stir in the butter, a few pieces at a time, until it is fully incorporated.
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Cool to room temperature.
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Using an electric mixer or wire whisk, whip the heavy cream into soft peaks. Gently fold a fourth of the whipped cream into the lime curd. Then fold in the remaining cream.
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To serve:
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Cut the cooled cake into squares and top with a generous dollop of lime cream.