In a shallow bowl, whisk together the cooled espresso, rum, and sugar until the sugar is dissolved.

In a large mixing bowl, beat the mascarpone cheese, pumpkin puree, powdered sugar, vanilla, and pumpkin pie spice until smooth and creamy.

In a separate chilled bowl, whip the heavy cream until stiff peaks form. Gently fold the whipped cream into the pumpkin mascarpone mixture using a spatula until no white streaks remain.

Quickly dip each ladyfinger into the espresso mixture for 1-2 seconds per side. Do not over-soak or they will become mushy.

Arrange a single layer of dipped ladyfingers in the bottom of an 8x8 inch baking dish.

Spread half of the pumpkin mascarpone mixture evenly over the ladyfingers, smoothing it out with an offset spatula.

Repeat with a second layer of dipped ladyfingers and top with the remaining pumpkin mixture.

Cover the dish with plastic wrap and refrigerate for at least 4 hours, or ideally overnight, to allow the ladyfingers to soften and flavors to meld.

Just before serving, dust the top generously with cocoa powder using a fine-mesh sieve.