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1
Coat the bottom and sides of a 7-by-11-inch glass or ceramic baking dish with the butter.
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2
Set aside.
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3
Pour the hot coffee into a medium bowl and add 3 tablespoons of the sugar.
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4
Stir until the sugar is thoroughly dissolved, then set aside to cool.
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5
Place the egg yolks in a medium bowl, add 4 tablespoons of the sugar, and beat with a whisk until the mixture is pale and creamy, about 2 minutes.
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6
Add the mascarpone and beat with the whisk, making sure to eliminate all lumps, until smooth and well combined.
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7
Place the egg whites in a separate bowl and, with a clean whisk, beat until theyre frothy, about 1 minute.
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8
Add a pinch of salt and the remaining 4 tablespoons of sugar and beat until you lift the whisk from the bowl and see a soft peak that slowly slumps, about 3 minutes.
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9
Using a rubber spatula, carefully fold the egg whites into the mascarpone mixture.
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10
Stir in the rum, if using.
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11
Dip the ladyfingers in the coffee and, one by one, lay them flat in the prepared dish.
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12
Once the first layer of cookies has been laid out, spread a layer of the mascarpone cream on top and dust with 2 tablespoons of the cocoa powder.
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13
Repeat to form a second layer in the dish.
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14
Sprinkle the top with the remaining 2 tablespoons of cocoa powder.
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15
Cover with plastic wrap (be careful to avoid letting it touch the top) and refrigerate for about 3 hours so the flavors and textures can marry.
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16
Cut into 8 squares and serve.
