Heat a grill or a heavy ridged pan to high. The corn needs direct contact with hot metal or flame to char rather than steam.
Stir the mayonnaise, sour cream, lime juice and salt together in a shallow dish wide enough to roll a cob in.
Grill the husked corn, turning every 2 to 3 minutes, for 10 to 12 minutes total, until kernels are blistered and blackened in patches all round.
Move the hot cobs straight into the sauce and roll to coat completely. Hot corn grips the sauce; cooled corn sheds it.
Roll each coated cob in the crumbled cotija on a plate, pressing lightly so it sticks.
Dust with chili powder, scatter with cilantro, and serve with extra lime. Eat immediately, with a skewer or the husk pulled back as a handle.