Heat 1 teaspoon olive oil in a small pan. When hot, add the thinly sliced red onions and sauté for about 5 minutes until soft. Remove from the heat and set aside.
In a small bowl, combine the shredded chicken breast and barbecue sauce. In a separate bowl, combine the mozzarella and cheddar cheeses.
Now it’s time to assemble your grilled cheese. To assemble each sandwich: Brush one side of each piece of bread with olive oil (about 1 teaspoon per piece). Place the bread oil-side down on a cutting board. Top one piece of bread with 1/3 cup of cheese and 1/3 cup of barbecue chicken. Add 1/3 of the sliced avocado, and then add 1/3 of the onions and 1 tablespoon of cilantro leaves. Top with another 1/3 cup of cheese in an even layer and add the second piece of bread with the oiled side facing out (duh).
Heat a large non-stick pan or skillet over medium heat. When hot add the sandwiches and cover with a lid. Cook for about 4 minutes until the underside is golden brown. Flip the sandwiches and cook for 3-4 minutes more.
Remove your grilled cheese from the pan and serve immediately with extra barbecue sauce or ranch dressing for dipping.