How to Make It
Roast the red and yellow bell peppers directly over a gas flame or under the broiler until they are charred all over. Transfer the peppers to a bowl, cover with plastic wrap and let cool. Peel, core and seed the peppers, then cut them into 1/2-inch dice.
Prepare an ice water bath. In a large saucepan of boiling salted water, cook the calamari over high heat until white and firm, about 1 minute. Drain and chill in the ice bath. Drain and pat dry.
In a small bowl, whisk the red wine vinegar with the anchovy paste and a generous pinch each of salt and pepper. Gradually whisk in the olive oil until the vinaigrette is emulsified.
On a work surface, mince the parsley with the minced lemon zest and garlic. Transfer the gremolata to a bowl.
In a large bowl, toss the arugula with 1 tablespoon of the vinaigrette. Season with salt and pepper and arrange on a large platter. Add the remaining vinaigrette to the bowl and toss with the roasted peppers, calamari, sun-dried tomatoes, olives, capers, shallot, and 3 tablespoons of the gremolata. Season the salad with salt and pepper and spoon over the arugula. Sprinkle with the remaining gremolata and serve.