Preheat the grill to medium high heat. Pull the husks back gently and rub the corn on all sides with butter then season with salt.
Grill the corn for about 15 to 20 minutes, rotating the corn every occasionally until the corn begins to char in places. Set the corn aside to cool slightly.
For the cilantro aioli:
In a small mixing bowl, whisk together the mayonnaise, garlic, lime zest and lime juice. Using a mortar and pestle, mash the cilantro so that it forms a paste.
Whisk the cilantro paste into the mayonnaise, cover and refrigerate until ready to use.
To serve:
Slather the charred corn all over with the cilantro aioli. Sprinkle the chili powder and cayenne over the corn followed by the cotija cheese. Serve warm with a side of lime wedges.
Notes
To serve the corn off the cob (esquites): once the corn is cool, stand the corn on its end and use a serrated knife to cut the kernels off the cob. Repeat with the remaining corn and discard the cobs. Gather all of the kernels in a medium mixing bowl and toss with the aioli and chili powder and top with the cotija. Serve with lime wedges.For an extra smoky flavor, use a cast-iron skillet on the stovetop or a grill pan if a backyard grill isn’t available.