Slit the squid tubes on one side. Remove the tentacles into a small bowl. Open up and place the squid flat onto a chopping board then lightly score them. Season with salt and pepper and rub them with olive oil. Squeeze a drop of lemon juice on top.
Preheat a barbecue or a ridged griddle pan.
Chop the parsley, zest & juice the lemon and chop the garlic. Put all in a mortar and grind it into a paste with the pestle, adding some olive oil gradually. The sauce should be textured and a bit oily. Season with salt and pepper. Set aside.
Cook the squid for 2-3 minutes on each side, then put them in a serving dish. Pour over most of the paste immediately and toss. Use the remaining sauce to marinate the tentacles, which you can fry in a drying/griddle pan (or BBQ in a aluminium tray).
Serve warm, room temperature or cold. Chill, if you want to serve it later.