Fill a large bowl or your largest pot with enough cold water to completely submerge the corn.
Pull away the outermost layer of the husks. With scissors or kitchen shears, trim off the topmost part of the husks up to the cob, including the silk tassel. Place the ears in the water. Let sit for at least 10 minutes or up to 8 hours (this will keep the husks from burning).
Heat a gas or charcoal grill to medium (about 350 to 400°F).
Remove the corn from the water and shake off excess. Place the corn on the grill, cover, then grill for 15 to 20 minutes, turning it every 5 minutes or so to ensure the corn cooks evenly. When the corn is done, the kernels should be tender when pierced with a thin, sharp knife.
Meanwhile if making the Mexican corn, in a small bowl, melt the butter. Stir in the Parmesan, chili powder, chipotle chile powder, cumin, and salt. Zest the lime directly into the bowl, then cut the lime into wedges. If making classic corn, skip this step and butter and season the corn directly.
Let the corn cool for at least 5 minutes. When cool enough to handle, peel back the husks and remove any stuck-on bits of silk (any remaining silk should come away easily, but if it is stubborn, it can be rubbed away with a kitchen towel).
Brush the grilled corn all over with the Mexican butter; serve hot with a wedge of lime to squeeze over the top. Or for classic corn, butter the corn and season with salt and pepper as desired.
Notes
*I prefer to grill corn with the husks on. The husks add flavor and help the corn steam, then char perfectly. That said, you can also make yummy grilled corn with the husks removed (the corn will be a little less tender and more charred). Remove the husks/silk from the outside of the corn and rub with olive oil. Grill on all sides over medium heat, turning every few minutes as the corn starts to char, until browned and tender, about 7 minutes. Season as desired.
If you prefer to serve the corn cut away from the cob, cut away the kernels and place in a large bowl. Stir together with the butter and seasonings. Serve right from the bowl.
TO STORE: Refrigerate leftover grilled corn for up to 4 days.
TO REHEAT: Arrange the corn on a parchment-lined baking sheet. Reheat in a 350°F oven for 4 minutes, flip the corn over, then continue cooking for a few minutes longer, until heated through. You also cut the corn away from the cob and reheat it in a skillet or the microwave.
TO FREEZE: Cut grilled corn away from the cob and transfer to a freezer safe ziptop bag. Freeze for up to 1 month.