Beat the mascarpone, sugar, and vanilla until smooth. Whip the heavy cream to stiff peaks, then fold into the mascarpone in two additions until no streaks remain.

Mix the espresso and rum in a shallow dish. Quickly dip each ladyfinger (1–2 seconds per side) and set aside.

In a 9-inch springform pan lined with parchment, arrange one layer of dipped ladyfingers. Spread half the cream over them. Repeat with a second layer of ladyfingers and the remaining cream. Smooth the top, cover, and refrigerate at least 6 hours, preferably overnight.

Release the pan sides, dust the surface heavily with cocoa, and top with chocolate curls. Slice and serve cold.