1. Line a 9 1/2-by-5-inch loaf pan with plastic wrap, leaving a 2-inch overhang on each side. Line plastic with parchment paper, leaving a 3-inch overhang on each long side. Set aside.

2. Pour syrup into a large, shallow dish. Cut cake into three strips: two 9 1/2 by 4 1/4 inches, one 9 3/4 by 4 3/4 inches; discard scraps. Soak one smaller strip in syrup 1 minute. Turn; soak 40 seconds more. Using two spatulas, carefully transfer cake to pan; gently press into bottom. Brush with about 3 tablespoons syrup.

3. In the bowl of an electric mixer fitted with the paddle attachment, beat the strawberry ice cream on medium speed until smooth, about 30 seconds. With a small offset spatula, spread in a smooth layer to cover cake layer. Repeat soaking process with other small piece of cake; place on top of strawberry ice cream, gently pressing down to level layer. Brush with syrup. Freeze about 30 minutes.

4. Remove pan from freezer. Repeat process to make a layer of pistachio ice cream and final layer of cake. Cover; place in freezer to harden completely, at least 3 hours or overnight.

5. Just before serving, whip heavy cream, sugar, and vanilla to soft peaks in a medium bowl. Invert pan onto a serving platter, and pull on plastic wrap to release cake from pan. Peel off plastic and parchment. Mound whipped cream on top, and spread with a rubber spatula. Cut into slices, and serve immediately.