In a medium bowl, combine chopped cilantro, olive oil, fresh lime juice, minced garlic, lime zest, salt, pepper, ground cumin, and cayenne pepper. Mix thoroughly with a whisk until well blended.

Coat the boneless, skinless chicken breasts evenly with the marinade, ensuring every piece is well covered. Allow the chicken to marinate at room temperature for about 30 minutes.

Preheat a large skillet over medium-high heat. Add the marinated chicken breasts and cook for about 4 minutes on each side until the internal temperature reaches 165°F.

In the same skillet, add a splash of olive oil if necessary, followed by chopped onion and diced red bell pepper. Sauté the vegetables for about 5 minutes.

Stir in the long-grain rice, ensuring it's well mixed with the sautéed vegetables. Then add chicken broth, petite-diced canned tomatoes, diced green chiles, additional cilantro, and a squeeze of lime juice. Bring this mixture to a simmer.

After the rice is cooked, dice the reserved chicken and add it back into the skillet along with drained black beans and shredded Monterey Jack cheese. Stir everything together and cover.

Once everything is heated and combined, remove the skillet from heat. Garnish your dish with additional chopped cilantro and serve immediately.