In the bowl of a stand mixer, add pumpkin puree, brown sugar, and ½ cup of granulated sugar. Whisk to combine.
Add the ginger, cloves, 1 teaspoon of cinnamon, nutmeg, and salt. Whisk to combine.
Add the mascarpone cheese and heavy cream. Whisk on medium-high until soft peaks form.
In a separate medium bowl, add the cooled espresso and ¼ cup of sugar. Whisk to combine.
Assemble tiramisu by dipping the ladyfingers in the espresso and lining half of them on the bottom of a 9x13-inch baking dish. Add a layer of the pumpkin cream mixture and spread it evenly over the top of the ladyfingers. Add another layer of the remaining espresso-dipped ladyfingers, as well as another layer of pumpkin cream mixture. Sprinkle with the remaining ½ teaspoon of cinnamon.
Refrigerate for at least 2 hours before to ensure that the ladyfingers will soak up all the flavors. The dessert is ready to slice and serve after that.