Preheat a grill to medium-high heat, around 400°F. Once hot, clean the grill grates. Remove the husks and silk from the corn. Pour about 1 teaspoon of vegetable oil on each corn cob and rub the oil onto all sides. Very lightly sprinkle salt and pepper on all sides of the corn. (The cotija cheese is quite salty, so you don’t want to add too much salt.) Place corn on grill grates (nothing needs to go down first; don’t wrap in foil) and close grill. Cook for about 3 minutes per side undisturbed. Using tongs, rotate and continue cooking, about 12 minutes total. When all sides are browned, remove onto a plate.
While corn is grilling, whisk together the sauce. Add the Mexican crema, mayo, cilantro, garlic, chili powder, paprika, cumin, cayenne pepper, 1 and 1/2 teaspoons lime zest, and 2 tablespoons lime juice to a bowl; whisk to combine. Taste and adjust any seasonings to preference.
Using a spoon or pastry brush, brush on the sauce, generously coating each ear of corn. Sprinkle on cheese, and if desired, an additional sprinkle of chili powder. Serve immediately with lime wedges.
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Notes
Storage: Store leftover elote in an airtight container in the fridge for up to 3 days. Reheat on the stovetop or in the oven until warm, or slice the kernels off and enjoy them cold in salads or bowls.