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Put your freezer on the fast-freeze setting, or clear some space in the coldest part of the freezer. Heat oven to 180C/160C fan/gas 4. Line a 23 x 33cm Swiss roll tin with baking parchment, grease with a little butter and set aside.
First, make the sponge. Put the egg yolks and sugar in a large bowl and whisk with an electric whisk until thick and creamy. Sift the cocoa powder over the egg mixture and whisk in thoroughly. Wash and dry the beaters. In a clean bowl, whisk the egg whites until stiff but not dry. Fold a third of the egg whites into the cocoa mixture, then gently fold in the rest until evenly distributed.
Pour into the prepared tin and spread gently with a spatula. Bake in the centre of the oven for 25 mins or until well risen and just beginning to shrink away from the sides of the tin. Remove from the oven, loosen the edges with a round-bladed knife and leave to cool in the tin.
Prepare the filling while the cake is cooling. Place a large sheet of cling film on the work surface, take the ice cream out of its tub and place on top. Working quickly, cover the ice cream with cling film, then press and roll into a long sausage shape. It will need to be 33cm long and around 5cm wide. Wrap a second piece of cling film around the first and twist the ends to maintain the sausage shape. Return to the freezer to harden for at least 1 hr.
Line a baking tray with baking parchment. Take the ice cream out of the freezer, unwrap it and place in the centre of the sponge. Using the parchment to help you, bring up the sides to enclose the ice cream and carefully lift the roll onto the lined baking tray, rotating it so the seal is underneath. Trim the ends. Cover the cake and tin with cling film and place in the freezer for at least 4 hrs, or up to 1 week.
Make the meringue topping 20 mins before serving. Put the sugar and 175ml water in a pan and bring to a rolling boil over a high heat. Continue to boil until it reaches 115C on a sugar thermometer.
Meanwhile, put the egg whites in a large mixing bowl or tabletop mixer and whisk the egg whites to soft peaks. Continue whisking at high speed and very slowly trickle in the hot sugar syrup. The meringue will begin to thicken and become glossy after about 10 mins. Continue to whisk until it is just warm, then whisk in the vanilla extract. Use the meringue immediately, as it is easier to work with while warm.
Fit a large piping bag with a 1.5cm star nozzle and fill with the meringue. Take the baking tray out of the freezer and slide the log gently onto a serving platter using a couple of spatulas. Pipe the meringue in lines down the length, then around the ends. Use a cook’s blowtorch to scorch the meringue all over. Alternatively, bake for 8 mins at 220C/200C fan/gas 7 or until the meringue is set and lightly browned. Serve in generous slices (it will sit quite happily for 5-10 mins). Please note this recipe contains lightly cooked egg whites, which may be unsuitable for babies and toddlers, the elderly, pregnant women and people who already feel unwell.