In a large bowl, combine the citrus juices and zest, herbs, soy, chilli, grated ginger and sugar.
Add the extra virgin olive oil and sesame oil and mix well until combined. Season to taste with salt and freshly ground black pepper.
Remove the tentacles from the squid and set aside. Place a flat wooden spatula inside the one of the squid tubes, lay it on a chopping board then score across the flesh at 5mm/½in intervals with a sharp knife. Repeat with the rest of the squid.
Heat a griddle pan over a high heat until smoking hot. While the griddle pan is heating, rub the squid with the olive oil and season with salt and freshly ground black pepper.
Place the squid tubes scored-side down into the griddle pan and cook for 1-2 minutes.
Remove the pan from the heat, flip the squid tubes over and leave for a further 30 seconds, or until just cooked.
Remove the tubes from the pan, place into the bowl with the dressing and turn gently to coat.
Return the griddle pan to the heat and cook the tentacles for 1-2 minutes, or until they start to crisp up on the edges. Transfer the tentacles to the bowl and turn to coat with the dressing.
Gently mix the salad leaves into the squid and dressing and arrange on serving plates.