Follow the chocolate and cherry ice cream recipes to make a batch of ice cream (yield: 1.5 pints). You will most likely need to make the chocolate ice cream a day in advance since many ice cream maker's freezing bowls takes a day to freeze before making another batch of ice cream.
Separate the Oreo cookies from the cream filling. Set the filling aside and place the Oreo cookies into a plastic bag and crush to a fine crumble. In a mixing bowl, combine butter and cookie crumble until evenly mixed. Transfer the cookie mixture into a pie dish and press down firmly into an even layer. Bake in a preheated oven preheated to 350 F for 10 minutes.
Top the crust with chocolate ice cream; distribute into an even layer; freeze for 2 hours. Then, top with cherry ice cream and distribute into an even layer; freeze for 30 minutes, until no longer extremely liquid.
Meanwhile, whip the heavy cream with the Oreo cream filling until they form firm peaks. Transfer to a piping bag fitted with a star-shaped piping tip. Pipe star-shaped whipping cream dollops around the edge. (try to pipe an even number.) Top every-other dollop with an Amarena cherry. In the center, sprinkle generously with chocolate shavings.
Dip a sharp knife into hot water to cut the pie into slices before serving.