Adjust broiler rack so that it is in position closest to flame and place a baking sheet on rack. Preheat broiler to high. Rinse chicken, then pat dry with a paper towel. Season all over with salt and Tuscan heat spice.

Heat a large drizzle of olive oil in a large pan over medium-high heat (use a nonstick pan if you have one). Add chicken and cook until browned and no longer pink in center, about 2 minutes per side. Remove from pan and let cool slightly, then cut into bite-size pieces.

Wash and dry all produce. Cut any large broccoli florets into bite-size pieces. Core, seed, and dice tomato. Heat a drizzle of olive oil in same pan over medium-high heat. Add broccoli and tomato. Cook, stirring, until just tender and wilted, about 3 minutes. Season with salt and pepper.

Scatter mozzarella in an even layer over flatbreads, followed by chicken, broccoli, and tomato. Carefully remove baking sheet from broiler and sprinkle with a drizzle of olive oil. Place flatbreads on sheet and sprinkle each with a drizzle of olive oil.

Carefully return sheet to broiler and broil flatbreads until cheese melts and crust starts to brown, 3-4 minutes. TIP: Check flatbreads occasionally for any burning.

Remove flatbreads from broiler. Sprinkle with another drizzle of olive oil and season with salt, if desired. Let flatbreads rest for 1 minute, then cut into slices and serve.