Use soaked chopsticks either stuck together or pulled apart and shove in the center of the trimmed bottom of each cob.
Preheat a grill pan or turn flame on medium-high. Rub corn with oil and place on the grill pan or use chopsticks as a handle and rotate corn above flame, avoiding direct contact between the flame and the chopstick handle. Rotate and cook corn on all sides until charred, about 6-10 minutes total. Remove corn from grill and, using a rubber spatula, spread mayonnaise on each cob on all sides. Sprinkle all sides with Cotija cheese, a pinch of cayenne pepper and a squeeze of lime. Serve warm.