If using whole graham crackers, place 6 whole graham cracker sheets in a large zip-top bag. Seal the bag and crush with a rolling pin into fine crumbs (about 1 cup).
Melt 3 tablespoons unsalted butter in a large frying pan over medium heat. Add the graham cracker crumbs and 1 pinch kosher salt, and cook until fragrant and the crumbs are toasted and crunchy, about 2 minutes. Remove the pan from the heat and let cool while you make the filling and topping.
Place ½ cup of the cold heavy cream, 2 ounces of the cold mascarpone cheese (about ¼ cup), and 2 tablespoons of the packed brown sugar in the bowl of a stand mixer (or medium bowl if using an electric hand mixer or making by hand). Beat with the whisk attachment on medium speed until soft peaks form, about 2 minutes. Transfer to another bowl (or leave in the bowl if using a hand mixer or making by hand).
Place the remaining 6 ounces cold mascarpone cheese (generous ¾ cup), remaining ⅔ cup packed brown sugar, 1 cup pumpkin purée, 1 ½ teaspoons pumpkin pie spice, and ¼ teaspoon kosher salt in the now-empty bowl (or large bowl if using an electric hand mixer or whisking by hand). Beat with the whisk attachment on medium speed, scraping the bowl down about halfway through with a flexible spatula, until smooth, 1 to 1 ½ minutes total. Scrape down the bowl again.
Add the remaining 1 cup cold heavy cream and 1 teaspoon vanilla extract, and beat on medium speed until soft peaks form, 1 to 1 ½ minutes.
Divide the graham cracker crumbs between 6 (6 to 8-ounce) glasses, jars, or ramekins (about 3 tablespoons per glass). Transfer the filling into a large zip-top bag and snip off one bottom corner; pipe the filling over the crumbs (generous ½ cup per glass); use the back of a small spoon to smooth the top in each glass.
Spoon the whipped cream over the filling (about 3 tablespoons per glass). Refrigerate for at least 2 hours or up to overnight. Dust lightly with more pumpkin pie spice before serving.