In the bowl of a stand mixer fitted with wire whisk, add pumpkin puree, pumpkin pie spice, salt, cream cheese and ¾ cup powdered sugar until pale and fluffy, about 2 minutes on high speed. Scrape down the sides of the bowl as necessary. Use a silicone spatula to transfer whipped pumpkin to a medium bowl.
Rinse the bowl of your stand mixer. In the same bowl, whisk the heavy cream with the remaining ¼ cup powdered sugar on high speed until soft swoops develop, about 2 minutes. Be careful not to overmix.
Divide half of the whipped pumpkin between 6 parfait glasses. Top with half of the whipped cream, divided among the glasses evenly. Follow up with a generous sprinkling of crushed graham cracker. Repeat the layering process again: whipped pumpkin, whipped cream, graham cracker crumbs. Serve immediately. Whipped pumpkin and whipped cream can be prepped ahead; assemble just before serving for the best texture and crunchy crumbs.