Preheat the oven to 180℃ fan / 200℃ / 356℉ convection / 392℉.
Line a 23 x 33 cm (9 x 13 inch) tin with baking paper.
Beat the eggs and sugar with the lemon zest and vanilla in a stand mixer or with hand mixers for 5 minutes until thick, light and tripled in volume.
Mix the flour with the salt and then lightly fold this into the egg mixture.
Pour the batter into the tin, spreading it out with a spoon to the corners of the tin.
Bake for 10-12 minutes, until the sponge springs back when gently pressed in the middle, or a skewer or toothpick inserted into the sponge comes out clean.
While the sponge is in the oven, lay a clean damp tea towel on the work surface. Top with a sheet of greaseproof paper that is slightly larger than the baking tin, and sprinkle the 1 tablespoon of caster sugar in an even layer all over the greaseproof paper.
Using oven gloves, carefully tip the hot cake out on to the greaseproof paper / baking parchment, gently peeling off the baking paper that the cake was cooked on.
Score a line across one narrow edge of the sponge 1-2 cm (½ inch) from the edge, with a sharp knife, taking care not to cut all the way through.
Starting at the end where you made the cut, tightly roll up the cake together with the baking parchment / greaseproof paper. Leave to cool.
Once the cake is completely cold, unwrap and remove the baking parchment / greaseproof paper. Spread with the lemon curd then roll the cake back up.
Place on a serving plate and dust with icing sugar / confectioners sugar. Best served the day it is made.