Step 1To prepare the corn, break off long hard stems and expose the ear by peeling back the husk without breaking it off at the base. Remove the silk by rubbing with your hands and a soft brush. Pull the husk back up over the ear to re-cover it. Soak the ears in cold water at least 20 minutes.
Step 2Grill the corn over a hot fire until it is dark yellow and the husks are well marked by the grill, about 15 minutes, turning occasionally to keep the husks from burning. Remove from the grill and set aside to cool.
Step 3Rub the inside of a large bowl with the cut garlic clove. Add the red onion and tomatoes. Using a sharp knife, cut the corn kernels cleanly from the cobs into the bowl. Do not scrape the cobs to get the last bits; that will muddy the appearance of the dish.
Step 4In a small bowl, whisk together the lemon juice, olive oil and salt. Place the arugula in a large bowl and toss it with enough of the dressing to coat lightly, about one-third of the total amount. Arrange the arugula on a platter.
Step 5Add the remaining dressing to the corn and tomatoes and stir together gently. Spoon the corn mixture loosely over the arugula, then use a vegetable peeler to shave cheese over the top. Serve immediately.