Combine 2/3 cups heavy cream, 4 ounces mascarpone cheese, vanilla extract, pumpkin puree, and 1 tsp pumpkin pie spice in a large bowl, or the bowl of your stand mixer.
Begin on low speed to avoid splashing, then gradually work up to beating the mixture at medium speed for 3 minutes, or until light and fluffy. Set aside.
In another large bowl, mix 1 cup heavy cream, 1/4 cup maple syrup, 1 tsp pumpkin pie spice, and brown sugar using an electric mixer. Beat slowly at first and gradually working up to medium speed. Mix until the whipped cream can hold a stiff peak.
Get ready for assembly by mixing the rum and espresso in a small bowl near your pan. Dip each ladyfinger into the rum mixture and lay them in an even layer along the bottom of your pan, using pieces to fill in as needed.
Spoon 1/3 of the pumpkin mousse over the ladyfingers and smooth it flat. Next layer on 1/3 of the whipped cream and smooth it flat as well. Repeat with 2 more layers of each the ladyfingers, mousse, and whipped cream, creating 9 layers total.
Dust the top of the tiramisu with cocoa powder. Chill at least 2 hours before serving cold.