Pat the squid bone-dry with paper towels and slice the tube open into a flat sheet. Score the inside shallowly in a diamond pattern, without cutting all the way through. This scoring does two things at once: the meat curls up beautifully in the pan and the heat penetrates faster, allowing you to cook the squid briefly enough to keep it tender. With squid, it is either cooked within two minutes or only becomes tender again after stewing for an hour; anything in between is rubber.
Boil the green beans in plenty of salted water for five to six minutes until al dente. Drain and plunge them into ice-cold water so they retain their bright green color and stop cooking. Pat them dry.
Halve the cherry tomatoes and slice the red onion into paper-thin half rings. Mix them with a tablespoon of olive oil, some lemon juice, and salt, and let them sit for a moment.
Heat a grill pan until smoking hot. Rub the squid with a tablespoon of olive oil, salt, and pepper, and grill for one and a half minutes per side until it has dark grill marks and is completely opaque. Slice it into wide strips.
Mix the green beans with the arugula, grated garlic, the remaining olive oil, plenty of lemon juice, and the chili flakes. Place the squid on top and finish with parsley and black pepper.