Firstly, we want to make sure the eggs are safe to eat. Combine egg yolks and sugar in a medium sized bowl and put it over a pot of simmering water (a bain marie), whisking continuously with a whisk or an electric hand mixer. The mixture should become pale and fluffy, the sugar should be dissolved and it should be fairly hot when you dip your fingertips in. If you have a thermometer, the mixture should reach just up to 70˚C (140˚F) to be considered pasteurized and safe to eat. Anything above that and your egg yolks will start to cook.
In a bowl of a standing mixer combine cold mascarpone, egg/sugar mixture, pumpkin puree, spices and vanilla extract. Mix on medium-high speed until it's all nicely incorporated. Add cold heavy cream and mix until everything is combined. Transfer to a large piping bag fitted with Wilton 6B nozzle.
Make strong coffee, transfer it to a shallow plate and let it cool, then add the rum and stir it all together. Dip one ladyfinger at a time, letting it soak 1-2 seconds on each side. Don't leave it for too long, otherwise they will turn into a mushy mess.
Place them in a 10-11 inch rectangle dish to cover the base. Then spread with half of mascarpone cream. Repeat the process of dipping again and then pipe the mascarpone cream on top. Dust with cocoa powder and put in the fridge for at least 4 hours to cool.
You can add more or less spices, to your liking.
This is the only recipe where all the ingredients don't need to be room temperature. It's actually better for mascarpone and heavy cream to be cold, because the cream won't whip up properly otherwise.
I use homemade butternut squash puree, but you can use whatever you have on hand. :)