CORN: Preheat a grill to medium-high heat, around 400 degrees 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 that oil onto all the sides. Very lightly sprinkle salt and pepper on all sides of the corn. (Remember, the cotija cheese is quite salty, so you don't want to add too much salt here.) Place corn on grill grates (nothing needs to go down first; don't wrap in foil) and close grill. Cook (temps remaining at 400F) for about 3 minutes per side undisturbed. Using tongs, rotate, and continue cooking, for about 12 minutes total. When all sides are browned, remove from the grill onto a plate.
SAUCE: While corn is grilling, whisk together the sauce. Add the Mexican crema, mayo, cilantro, garlic, chili powder, paprika, cumin, cayenne pepper, lime zest, and lime juice to a bowl; whisk to combine. Taste and adjust any seasonings to personal preference.
ASSEMBLE: 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.