To the canister of a food processor fitted with the S-blade, add the cilantro, green onions, about 4 tablespoons of olive oil, lime juice, salt, pepper, and the optional cayenne pepper. Mix on high speed until the cilantro and green onions are broken down and the mixture is emulsified. If necessary, add additional oil to get things moving in the food processor until the sauce comes together in a thick but pourable consistency. Taste and make any necessary seasoning adjustments if desired; set the sauce aside.
In a large skillet, add 2 tablespoons of olive oil. Next, add the chicken and season evenly with salt and pepper. Cook over medium-high heat for about 5 minutes, or until the chicken is cooked through. Stir and flip intermittently to ensure even cooking.
Once the chicken is cooked through, reduce the heat to medium-low. Drizzle about 1/3 cup of the cilantro sauce over the chicken, stir to coat evenly, and simmer gently for about 2 minutes; reserve the remaining sauce for serving.
Remove the chicken from the skillet and evenly divide the chicken, rice, beans, and tomatoes between the serving bowls.
Add additional cilantro sauce over the rice, beans, or tomatoes if desired. Enjoy your Cilantro Chicken with Rice and Beans!