Heat oven to 350° degrees. Line a baking sheet with foil; coat foil with nonstick cooking spray. Spread pumpkin onto greased foil. Bake at 350 degrees for 20 minutes. Remove from oven and cool slightly. Coat two large baking sheets with nonstick cooking spray. Set aside.
In a small bowl, whisk together the flour, cocoa, baking powder and pumpkin pie spice. Set aside. In a large bowl, combine baked pumpkin, butter and sugar. Beat with an electric mixer on medium speed until well blended. Beat in egg, then stir in flour mixture.
Drop batter by heaping tablespoonfuls onto prepared baking sheets. Bake at 350 degrees for 15 minutes. Remove cookies from oven; press down with a flat-bottom glass or measuring cup. Transfer to wire racks and cool completely. Repeat with all dough.
Once cookies are cool, place mini chips in a small bowl. Top one cookie with 3 tablespoons of the ice cream (on flat side of cookie). Press the flat side of another cookie into ice cream. Roll edge of sandwich in chips. Repeat with all cookies and ice cream, rolling half of the sandwiches in mini chips. Wrap each sandwich in plastic. Freeze at least 3 hours or overnight.