In a bowl, combine the coffee, 30 ml (2 tablespoons) of sugar and the rum. Keep in the refrigerator.
In a food processor, combine the mascarpone, 125 ml (1/2 cup) sugar, pumpkin purée, and spices until the texture is smooth, about 2 minutes. Set aside.
In another bowl, whip the cream with the remaining sugar until stiff peaks form. With a spatula, gently fold into the cheese mixture.
Quickly soak the cookies into the coffee mixture. Place half the cookies at the bottom of a large serving bowl or a 20-cm (8-inch) square dish. Cover with half the cheese mixture and layer with the remaining cookies and filling. Refrigerate for 2 hours before serving. Sift the cocoa powder over the surface. Refrigerate for at least 2 hours or overnight.