Spoon the chocolate ice cream in small pieces into a 9-inch springform pan, lined with plastic wrap, filling in any large holes, then spread it evenly with a warm rubber spatula. Heat cream and stir in Nutella to thin out. Cool. Pour 1/2 of the Nutella over the chocolate ice cream and spread it evenly with a small offset spatula. Freeze for at least 1 hour, or until firm.

Spoon the strawberry ice cream over the Nutella in small pieces, filling in any large holes, then spread it evenly with a warm rubber spatula. Pour the remaining Nutella over the ice cream and spread it evenly with the offset spatula. Scatter the hazelnuts over the top of the cake, then press in. Cover the pan tightly with aluminum foil and freeze for at least 6 hours, or up to 2 weeks.

To serve, let the cake stand at room temperature for 5 to 10 minutes or in the refrigerator for 15 to 20 minutes. Run a knife around the inside of the pan, release the side of the pan, and remove it. Cut the cake into wedges.