Place the corn, still in its husks, directly on the oven rack and roast for about 20 minutes until the corn is soft when you press on it. Take the corn out of the oven and let it cool a little until you can handle it, or until you're ready to serve.
When you're ready to eat, place a large grill pan on 2 burners over medium-high heat or preheat an outdoor gas or charcoal barbecue and get it very hot. Take a few paper towels and fold them several times to make a thick square. Blot a small amount of oil on the paper towel. Then carefully and quickly wipe the hot grates of the grill to make a nonstick grilling surface. When the grill or grill pan is hot, peel down the husks from the roasted corn and pull out the corn silk. Then tie the husks in a knot so you can hold on to the knot like a handle. Char the corn on the grill or grill pan, turning, until the kernels are slightly blackened all around and start popping, about 6 minutes. Brush the corn with mayonnaise, and sprinkle with the Parmigiano and a little cayenne pepper so it's nicely coated. Serve with lime wedges.