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1
Heat your grill to medium/medium-high.
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2
Cut the radicchio through the root end so each quarter has one fourth of the core.
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3
This will help keep each segment in tact.
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4
If any of the outer leaves do detach, simply grill them separately.
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5
Rinse the radicchio quarters, pat dry and set aside.
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6
Scrape the membrane off the squid bodies.
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7
Cut down one side of each body and unfold.
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8
With a paring knife, make a series of cuts, less than halfway into the flesh, along the length of the body.
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9
Now make another series of cuts diagonally crossing the first ones.
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10
Again, be very careful to not cut too deep or the squid will come apart.
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11
This procedure is known as scoring and will allow them to grill flat and not curl up.
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12
Brush the squid and the radicchio quarters with olive oil.
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13
Start by grilling the radicchio on one of the flat sides.
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14
Each side will take 2 to 3 minutes.
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15
Give them a head start and then start grilling the squid, turning once, until just cooked through and lightly golden, about 2 to 3 minutes.
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16
Do not overcook or it will become rubbery.
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17
Mix the arugula and red onion and place in the center of a large platter.
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18
Cut the calamari into strips and sprinkle over top of the arugula.
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19
Arrange the radicchio quarters around the pile of arugula.
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20
Whisk the olive oil, lemon juice, garlic and salt and pepper and drizzle over the salad.
