For the Swiss roll sponge, preheat the oven to 190C/375F/Gas 5 and line a 23x33cm/9x13in Swiss roll tin with baking parchment.
Place the eggs, sugar and vanilla seeds into a bowl and whisk until very light, fluffy and thickened.
Sift the flour over the mixture and fold in.
Pour the mixture into the lined tin and smooth it out with a spatula until evenly spread.
Bake the sponge for 10-12 minutes, or until just firm to the touch.
Place a sheet of baking parchment that is slightly bigger than the tray onto the work surface and dust with some caster sugar
Flip the sponge over onto the parchment paper, then peel off the parchment on the bottom of the sponge. Set aside to cool slightly.
Whip the double cream with the vanilla extract in a bowl until soft peaks form when the whisk is removed.
For the blackberry compôte, place the blackberries, sugar and four tablespoons of water in a small saucepan and simmer for five minutes, then leave it to cool and thicken.
To assemble the Swiss roll, spread the blackberry compôte over the cooled sponge, leaving a 2cm/1in gap around the edge.
Spread the whipped cream over the top of the jam and then sprinkle over the whole blackberries.
Take the longest edge, then using the parchment paper underneath to start it off, roll up the sponge quite tightly, making sure the filling stays inside. Roll the sponge off the parchment, dust with extra caster sugar and cut into slices to serve.