In a medium bowl, combine shredded cooked chicken with BBQ sauce, pickled jalapeños, and finely chopped red onion. Mix until the chicken is thoroughly coated.

Spread butter on one side of each slice of bread. In a cold skillet, place one slice of bread butter-side down. Add a layer of Monterey Jack cheese followed by half of the BBQ chicken mixture, topped with a layer of sharp Cheddar cheese.

Carefully place another slice of buttered bread on top, butter-side up. Turn skillet to medium heat and grill for about 3-4 minutes on each side.

After 3-4 minutes, flip the sandwich to grill the other side until both sides are toasted and cheese is melted, about another 3-4 minutes.

Once golden brown and cheese is melted, remove from skillet, sit for a minute, then cut in half and serve.