Place the corn, in its husks, directly on the oven rack and roast for 20 minutes until the corn is soft when you press on it.
To finish off the corn, peel down the husks, remove the corn silk, and tie the husks in a knot so you can hold on to it like a handle. Char the corn on a hot grill, over a gas flame, or under a broiler, until the kernels are slightly blackened all around and start popping, about 6 minutes. Rub the corn with mayonnaise, sprinkle with Parmesan and cayenne pepper so it's nicely coated. Serve with lime wedges.