Melt the chocolate with the cream, stirring until smooth. Mix two cups of the ice cream with the chocolate until well blended. Pour into the bottom of a 9x5 pan, smooth with a spatula, and freeze for about 2 hours.
Layer 2 cups softened vanilla ice cream over the chocolate layer and smooth with a spatula. Freeze for one hour or, if it is firm enough, add the strawberry layer right away.
Blend strawberries into a puree. (There should be about 1/4 cup.) Mix puree with the remaining vanilla ice cream. Pour over hardened vanilla layer, cover, and freeze for another hour before serving.
To serve, turn over and remove from pan onto plate. Cut into slices and serve with sweetened whipped cream, if desired.