Preheat the oven to 375°F.
Spread pine nuts on baking sheet and roast in middle oven rack 8–10 minutes until golden.
Meanwhile, cut zucchini into wide ribbons using potato peeler. Place zucchini in large salad bowl with arugula and mint. Set aside.
Heat grill pan or frying pan and when hot, add chorizo. Cook 4–5 minutes, turning halfway through, until chorizo caramelizes slightly at edges and releases oil. Remove chorizo from pan with slotted spoon, leaving oil in pan, and set aside.
Slice squid in half and then into fat strips. (Strips should be large because they will curl up and shrink when cooked.) Return pan with chorizo oil to heat and when sizzling, add squid and garlic. Season with salt and pepper and cook 2-3 minutes, tossing every so often. Add lemon juice, sun-dried tomatoes, and cooked chorizo then remove from heat and stir well.
Place ingredients in pan atop zucchini salad; dress with drizzle of olive oil and sprinkle of roasted pine nuts. Grate Parmesan over top in large flakes and season to taste. Toss salad well, garnish with additional Parmesan flakes, and serve.