Turn your oven's broiler up to high.
Peel off the outer layers of the corn and clean off all the corn silk. Leave the green ends attached for a convenient handhold.
Place the cobs on a baking pan under the broiler for 2 to 3 minutes, then rotate them and repeat until they're brown and toasty all the way around. The broiling shouldn't take more than 10 minutes total.
Working quickly, spread a tablespoon of mayonnaise over each cob, lightly coating every kernel. Next, sprinkle the cheese all over the corn. It should stick fairly easily to the mayonnaise, but you'll probably get a little messy coating them thoroughly.
Sprinkle chile powder over the corn, but not too heavy or it'll be gritty. Use any chile powder you like; ancho or cayenne are great.
Lastly, squeeze lime juice all over and serve hot!