Preheat the oven to 400 degrees F. Spread the walnuts out on a baking sheet and bake until toasted, about 8 minutes. Let cool, then finely chop.
Meanwhile, beat the heavy cream, pumpkin pie puree and confectioners' sugar together in a large bowl with an electric mixer until stiff peaks form, about 5 minutes.
Spread a fifth of the pumpkin mixture on the bottom of a 9-by-13-inch baking dish, followed by a layer of gingersnap cookies (4 cookies wide by 7 cookies long). Repeat 3 more times, for 4 layers of pumpkin and cookies. Finish with the remaining pumpkin mixture. Refrigerate for at least 4 hours or overnight. Sprinkle the chopped walnuts and mini chocolate chips on top of the cake right before serving.