Add mascarpone cheese, pumpkin, and pumpkin pie spice; beat just until filling is smooth.
Line bottom of 9-inch-diameter springform pan with 2 3/4-inch-high sides with 1 package ladyfingers, overlapping and crowding to fit.
Sprinkle with 2 tablespoons rum.
Spread half of filling over ladyfingers.
Repeat with second package ladyfingers, remaining 2 tablespoons rum, and remaining filling. Smooth. Wrap tightly in plastic, then foil. Chill overnight.
To unmold, run knife around inside edge of pan. Release pan sides; sprinkle with amaretti cookies.