Combine all of the ingredients except for chicken in a food processor; process until smooth. Place chicken breasts in a small baking dish. Pour marinade on top, turning to coat both sides of chicken. Cover and refrigerate for 3 hours.

Preheat grill-pan to medium-high heat.

Remove chicken from marinade and place in hot grill-pan. (Discard any remaining marinade.) Cook until done, about 5-6 minutes per side. Using 2 forks, shred chicken and set aside.

Preheat oven to 400°F.

Line 2 large baking sheets with parchment paper; set aside. (See note.)

Spread ½ cup of barbecue sauce across flatbreads, leaving ½” border on all sides. (Note: Use about 2 Tbsp of sauce per flatbread.)

In a medium bowl, combine the mozzarella, smoked Gouda, and cheddar cheeses. Sprinkle cheese mixture evenly on top of flatbreads.

Divide shredded chicken and sliced onions across the top of the flatbreads.

Bake at 400°F for 5-6 minutes.

Remove flatbreads from oven and top with fresh cilantro.

Drizzle remaining ¼ cup of barbecue sauce across tops of flatbreads.