Mix the espresso with the coffee liqueur and chill.
Melt the chocolate with 1/2 cup of cream over a double boiler, then let it cool.
Whip the remaining 1/2 cup (or 3/4 cup) of cream until stiff. Keep in mind that using more cream will increase volume but may dilute the flavor of the mascarpone.
Using a hand-held whisk (a stand mixer may be too powerful), whip the mascarpone with the sugar and rum until just combined. Avoid over-whisking, as this can cause the cheese to curdle. Gently fold the whipped cream into the mascarpone mixture. Chill until firm.
If using a sponge cake, cut it into three layers about 1 cm (½ inch) thick. I used to cut the cake into ½ cm (¼ inch) layers and sandwich them with chocolate ganache. The result was the best tiramisu ever, but it was too much work because the thin sponge layers broke easily.
Lay a layer of 10 sponge fingers in a glass dish or bowl (or use a slice of sponge cake on a serving plate). Spoon about 1/3 of the espresso over the fingers to soak. Spread 1/3 of the chocolate ganache over the cake, followed by 1/3 of the mascarpone mixture. Repeat the layers, finishing with a layer of mascarpone.
Sieve a thick layer of cocoa powder over the tiramisu and/or garnish with chocolate shavings. Chill overnight or for at least 12 hours.