Spoon softened ice cream into a 5cm x 30cm pipe and freeze for 4 hours until solid.
Preheat the oven to 190°C and line a 23cm x 33cm Swiss roll tin with parchment.
Whisk eggs and sugar in a bowl until light and thickened.
Sift the flour over the egg mixture and carefully fold it in.
Pour the batter into the tin and smooth it out evenly with a spatula.
Bake the sponge for 10 to 12 minutes until firm to the touch.
Dust a second sheet of parchment paper with caster sugar.
Turn the sponge onto the sugared paper and peel off the backing parchment.
Cook sugar, lemon zest, and juice in a frying pan until thickened.
Pulse strawberries in a food processor until roughly chopped.
Simmer strawberries with the sugar mixture for 5 minutes until thick, then cool.
Spread cooled jam over the sponge leaving a 2cm border.
Remove the frozen ice cream cylinder from the pipe using heat or water.
Place the ice cream on the sponge and roll it up tightly using the parchment.
Slice the roll and serve immediately.