Bring a large stock pot filled with water to a boil. Place shucked ears of corn into the water and boil for 7 minutes. Remove corn from water with tongs and set aside.
Put the water-filled pot that you boiled the corn in over high heat, and bring it back to a boil.
Add thawed, cleaned and sliced calamari to boiling water and cook for 3 to 4 minutes to desired doneness, then strain into an ice bath. Cool completely and drain thoroughly.
Place cooked squid in a bowl.
Mix dressing ingredients and pour over squid. Let marinade in the refrigerator for at least an hour.
Put arugula and prepared vegetables on platter. Shave the corn kernels off of the cobb and sprinkle the chunks of kernels over the rest of the vegetables.
With a slotted spoon, remove the squid from the dressing, and place it over the top of the vegetables.
Pour the remaining dressing into a bottle so people can add to their salad if they wish.
Refrigerate leftover dressing for up to one week.