How to Make It
Slit the squid bodies lengthwise and open them on a work surface. Score a cross-hatch pattern on the insides and transfer to a bowl. Fold in the tentacles, the grated citrus zests and 1 teaspoon of the red-pepper flakes and 1/4 cup of the olive oil. Refrigerate for 1 hour.
Meanwhile, in a food processor, combine the parsley, anchovies, garlic, capers and shallot and pulse until finely chopped. Add 1/2 cup of the olive oil and pulse to a coarse puree. Add the vinegar and the remaining 1/4 teaspoon of crushed red pepper and season the salsa verde with salt and pepper.
Light a grill or preheat a grill pan. Season the squid with salt. Grill over high heat, turning once, until charred in spots, about 5 minutes. Transfer all of the squid bodies to a work surface and thinly slice them. Transfer the squid to a medium bowl and toss with half of the salsa verde.
In a large bowl, whisk the remaining 1/4 cup of olive oil with the lemon juice and season with salt. Add the arugula, melon, celery and fresh chile and toss gently. Add the squid and toss again. Transfer the salad to a platter or plates and serve the remaining salsa verde on the side.