Remove the husks and then rinse each piece of corn to get rid of all the silk from the cobs or use a silker brush. Set aside.
In a small bowl, melt the butter and set aside.
In a separate small bowl, squeeze the juice of the limes and set aside.
Combine the chili powder, smoked paprika, salt, and pepper, mix well. Place in a separate small bowl.
Crumble the Cotija cheese and place in a separate bowl. If you're using mayonnaise, place it in a separate bowl.
Using a basting brush, baste the melted butter onto each cob on all sides.
Generously sprinkle each cob with the chili powder, paprika, salt, pepper, and cayenne (if you are adding it.)
Place each corn on the cob on a grill and grill for about 15 minutes or until the kernels start to turn a light brown color. Lightly sprinkle on some Cotija cheese and allow it to grill for 2-3 more minutes.
When done, remove from the grill. Take the basting brush and baste on more of the lime juice onto each cob, along with a bit more melted butter and mayonnaise (optional).
Top with additional cotija cheese and serve immediately.