In a small saucepan, heat the water, sugar, vinegar, and salt. Place the onions in a heatproof bowl, cover with the vinegar mixture and cool at room temperature.
Combine all of the dressing ingredients except the oil in a blender or with a whisk. With the motor running, drizzle in the oil until emulsified. Season with salt and pepper.
In a small bowl, toss together all of the dill chickpea ingredients.
In a large bowl, toss together the lettuces, tomatoes, pepperoncini, fennel, sopressata, mozzarella, artichoke hearts, dill chickpeas, pickled red onions, and vinaigrette. Toss to combine thoroughly and serve.