Preheat a grill or grill pan. Grill the corn, turning frequently, to avoid over charring, about 10 minutes.
Let the corn cool just enough to handle and peel back the husks, leaving them attached at the bottom. (The husks are going to serve as handles when eating the corn.) Remove the corn silk and generously spread the ears with mayonnaise. Sprinkle the corn with the cheese and chile powder. Serve immediately.
In a food processor, blend the garlic, jalapeno, and lime. Add the egg and salt, to taste. While the motor is running, drizzle in the oil until a smooth sauce is formed. Store in the refrigerator until ready to use.
Preheat the oven to 400 degrees F.
Put the chiles on a small baking sheet and bake until browned, about 3 minutes. Let cool.
In a clean coffee or spice grinder, finely grind the chiles and transfer to a bowl. Stir in the salt and use as desired.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.