- Preheat the oven to 375 °F (190 °C). Line the bottom of a 10-x-15-inch (25 x 37 cm) jelly roll pan (a baking tray with a lip) with parchment paper.
- Place the eggs and ¼ cup (50 g) of the sugar in a large mixing bowl or in the bowl of a stand mixer fitted with a whip attachment and whip on high speed for a minute, so that the sugar dissolves.
- Place the remaining ½ cup (100 g) of sugar and the water in a small saucepan and bring to a boil over high heat. Boil the sugar, without stirring, until it reaches 239 °F (115 °C) on a candy thermometer, about 2 minutes. With the mixer (or beaters) on high, pour the sugar down the side of the bowl (this prevents the hot sugar from splashing) and continue to beat until the mixture cools and is pale and triples in volume.
- Sift the cocoa powder, flour and salt into the eggs and fold in quickly but gently (it will deflate a little as you fold). Pour the batter into the prepared pan and spread to level it. Bake the cake for about 15 minutes, until it springs back when gently pressed. Have a tea towel and the icing sugar handy for when it comes out of the oven.
- Let the cake cool for 1-2 minutes (but no more than 5) and then run a knife around the inside edge of the pan to loosen the cake. Dust the top of the cake with icing sugar and place the tea towel overtop. Flip the pan over, holding it with the tea towel and remove the tray. Carefully peel away the parchment paper, lightly dust with icing sugar and roll up the warm cake from the short end, rolling the tea towel in it as you go. Let this cool completely before filling.
- For the frosting, beat the cream cheese and butter using electric beaters or in a stand mixer fitted with the paddle attachment until smooth. Add the icing sugar and vanilla and beat in, starting on low speed and then increasing to medium-high, until the frosting is fluffy and light.
- Unroll the cooled cake and spread the frosting over it*. Roll up the cake from the short end, lifting it just a little bit as you roll, so that the frosting doesn’t get pushed out. Dust the top of the cake with icing sugar and chill until ready to serve.
*For a decorative option, reserve a bit of the filling before assembling the Swiss Roll. Spoon it into a piping bag fitted with a star tip and pipe a swirling pattern along the top of the Swiss Roll before dusting with icing sugar.
The cake will keep, refrigerated, for up to 4 days.