For the ice cream cake: Butter a 9-inch springform pan and line it with a parchment paper circle. Cover the bottom of the pan with the pound cake, using any extra pieces to line the sides of the pan if desired.
Toss the strawberries with the granulated sugar and rum in a medium bowl, and then layer them on top of the pound cake. Scoop the ice cream onto the berry layer, packing it in tightly. Spread with an offset spatula to make a smooth top. Cover with plastic wrap and freeze until firm, 2 to 2 1/2 hours.
Unmold the cake by running a knife around the edge of it, then unhinge the springform and remove. Invert the cake onto a sheet of plastic wrap and remove the bottom of the pan and the parchment. Place a plate on the bottom and invert once more.
For the strawberry whipped cream frosting: Add the heavy cream, confectioners' sugar, strawberry jelly and vanilla to a large bowl and whip with an electric mixer until soft peaks form. This makes enough frosting to cover the top and sides of the cake with additional to pipe decorations if desired.
Frost the top and sides of the cake with the whipped cream frosting. Sprinkle with the amaretti cookies. If the cake begins to get too soft, put it back into the freezer for a few minutes.
Freeze another 1 1/2 to 2 hours or overnight. Before serving, let the cake sit at room temperature for about 20 minutes.
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