Cut a 24-by-6-inch strip of parchment paper. Butter the side of an 8-inch springform pan, then line the side with the parchment; the paper will extend above the rim of the pan so you can build a tall cake.

Mix the crushed cookies, sugar and melted butter in a bowl until combined. Press the mixture into the bottom and about 1/4 inch up the side of the prepared pan. Freeze until firm, about 15 minutes.

Scoop the lemon sorbet over the crust in small batches, packing it in with an offset spatula; smooth the top. Freeze until firm, about 45 minutes. Repeat with the raspberry sorbet and freeze until firm, about 45 more minutes.

Place the chocolate in a heatproof bowl. Heat the cream in a small saucepan or in the microwave until barely simmering; pour the hot cream over the chocolate and let stand 1 minute, then stir until smooth. Remove the side of the springform pan and the parchment. Spread the chocolate mixture over the top of the cake and freeze until set, about 10 minutes. Serve immediately or cover and freeze for up to 2 days.

Photograph by Kana Okada