Assemble the cake: Place 1 cake layer on a platter; scoop the ice cream on top and spread it to the edge using an offset spatula. Top with the second cake layer, then run the spatula around the sides to smooth the ice cream. Freeze until firm, about 4 hours.

Make the topping: About 30 minutes before serving, remove the cake from the freezer and let stand at room temperature. Toss the berries and 3 tablespoons sugar in a bowl; set aside until ready to serve. Beat the heavy cream, the remaining 1 tablespoon sugar and the vanilla in a bowl with a mixer on medium speed until medium peaks form, 1 to 2 minutes. Spread on top of the cake. Top with the berries and their juices.

Photograph by Levi Brown