Prepare a charcoal grill.
Grill the corn and peppers 4 in. from the hot coals, turning occasionally until the skin of the peppers and the husks of the corn are black and corn kernels are a light golden, about 6 - 10 minutes.
Remove the peppers from the grill and place them in a paper or plastic bag. Close the bag tightly and let cool for about 10 minutes.
Remove the corn from the grill and let cool. Remove the husks and silk from the corn. Cut the kernels from the cob and set aside.
Scrape the blackened skin from the peppers with a knife and reserve. In a blender, puree the pepper, tomatoes, garlic, vinegar and olive oil. Season with salt and pepper to taste and strain through a fine mesh strainer into a bowl and reserve.
Toss the corn and arugula in a bowl and distribute among six plates. Garnish with olives and cherry tomatoes. Shave the Parmigiano over the top of the salad.