Add the olive oil, 1 large chipotle pepper, 2 tablespoons lime juice, ½ teaspoon smoked paprika, and 1 teaspoon salt to a gallon-sized zip-top bag. Squeeze the bag to mash up the chipotle pepper until it's incorporated into the marinade. There will still be some chunks remaining.
Add the corn to the bag and seal it. Roll the ears of corn in the bag to coat with the marinade. Set aside while you prep the crema.
Add the sour cream, mayonnaise, remaining 2 tablespoons lime juice, ½ chipotle pepper, ½ teaspoon smoked paprika, and ¼ teaspoon salt to a small bowl. Stir to combine, breaking up the chipotle pepper with a fork or the back of a spoon. Set aside.
Preheat a grill to 400 F.
Place the marinated corn directly on the grill grate and cook for 10-12 minutes, turning halfway, until charred. Remove to a serving platter.
Coat each ear of corn with the crema mixture, turning the ears to coat completely.
Top the corn with the cotija cheese and cilantro before serving.