In a large bowl, whisk the pumpkin puree with the sugar, vanilla, salt, ground ginger, and ½ teaspoon of the ground cinnamon. Add the heavy cream and mascarpone. Using an electric hand mixer, beat the pumpkin mixture at medium speed until soft peaks form. Cover with plastic wrap or scrape into a pastry bag and refrigerate until ready to use.
In a small bowl, combine the chai tea concentrate and the rum, if using. Working one at a time, dunk the ladyfingers in the chai mixture until nicely saturated but not falling apart. Arrange half of the ladyfingers in the bottom of 6 small glasses (about 7-ounce capacity; see Notes), breaking them into pieces to create an even layer. Top with half of the pumpkin custard. (You can use a spoon or a pastry bag to do this.)
Repeat this process with the remaining ladyfingers and the remaining pumpkin custard, filling the glasses all the way to the top. Using an offset spatula or a knife, smooth the top of each glass. Cover loosely with plastic wrap and transfer to the refrigerator. Chill for at least 2 hours and up to overnight.
When you’re ready to serve, remove the tiramisu from the refrigerator. In a small bowl, whisk the cocoa powder with the cinnamon. Using a fine mesh sieve, dust the top of each tiramisu with the cocoa powder mixture. Enjoy!