Place goat cheese and cream cheese in a bowl, set aside.
Remove husk and silk from corn and rub with olive oil. Cut onion into 1/4" slices. Place corn and onions and grill. Cook until both are charred, turning corn and flipping onions as needed.
Returning to the cheese, stir cream cheese and goat cheese together. Once combined, stir in lime juice and vigorously whip the mixture until lighter. Chop cilantro and stir into the cheese.
Spread cheese mixture onto one entire side of the quesadilla. Layer onions and sprinkle corn on one half. Fold quesadilla over and return to grill. Cook on both sides until the tortilla is browning and crispy, 3-5 minutes depending on heat source.
Notes
*For a little extra kick, rub the sweet corn with a bit of chipotle powder before grilling.