Place the rum in a heatproof bowl and sprinkle the gelatin over it. Set aside for 10 minutes for the gelatin to soften.
In a large bowl, whisk together the pumpkin, granulated sugar, brown sugar, egg yolks, orange zest, cinnamon, nutmeg and salt. Set the bowl of gelatin over a pan of simmering water and cook until the gelatin is clear. Immediately whisk the hot gelatin mixture into the pumpkin mixture. In the bowl of an electric mixer fitted with a whisk attachment, whip the heavy cream and vanilla on high speed until soft peaks form. Fold the whipped cream into the pumpkin mixture.
To assemble, spoon some of the pumpkin mixture into parfait glasses, add a layer of whipped cream, then some chopped cookies. Repeat, ending with a third layer of pumpkin. Cover with plastic wrap and refrigerate for 4 hours or overnight. To serve, decorate with whipped cream and cookies.
Sweetened Whipped Cream
Whip the cream in the bowl of an electric mixer fitted with a whisk attachment (you can also use hand mixer). When it starts to thicken, ass the sugar and vanilla and continue to beat until firm. Don't overbeat!