Combine the pumpkin, cottage cheese, cream cheese, brown sugar and pumpkin pie spice in a food processor. Process until smooth.
Beat 1 cup whipping cream and 1/2 cup sour cream in a large bowl at medium-high speed until soft peaks form. Add 1 1/2 tablespoons of the sugar and continue beating until stiff peaks form. Gently fold the cream mixture into the pumpkin mixture.
Spray a 9x13-inch pan with nonstick cooking spray.
Combine the coffee and 1/4 cup sugar in a small bowl. Stir until the sugar dissolves. Dip both sides of the ladyfingers in the coffee.
Line the bottom of the baking dish with 16 ladyfingers, cutting if necessary to fit. Spread half of the pumpkin mixture over the cookies; repeat layers.
Beat ¾ cup whipping cream, ¼ cup sour cream and 1 tablespoon sugar together in a large bowl at medium-high speed until stiff peaks form. Spread on top of the dessert.
Cover and refrigerate for 6 to 8 hours (or overnight). Sprinkle with the cocoa right before serving.