Place a baking sheet on top rack (two baking sheets on top and middle racks for 4 servings) and preheat oven to 450 degrees. Wash and dry produce.

Core, deseed, and dice green pepper into ½-inch pieces.

Open package of chicken* and drain off any excess liquid.

Heat a large drizzle of oil in a large pan over medium-high heat. Add chicken and green pepper; season with salt and pepper. Cook, stirring, until chicken is browned and cooked through, 4-6 minutes.

Stir in BBQ sauce, then remove pan from heat.

Meanwhile, drizzle both sides of each flatbread with olive oil; brush or rub to coat all over. Season with salt and pepper. Carefully place flatbreads on preheated sheet. (For 4 servings, divide flatbreads between two preheated sheets. Toast on top and middle racks, swapping rack positions halfway through toasting.)

Toast on top rack until golden brown and crisp, 3-4 minutes.

Evenly top toasted flatbreads with BBQ chicken mixture, mozzarella, and cheddar.

Return to oven until cheese melts, 2-3 minutes. Transfer to a cutting board and slice each flatbread into quarters.

Divide flatbreads between plates. Drizzle with ranch dressing and serve.