Step 1Rinse the chicken breasts and pat dry. Season with cumin, oregano, salt, and pepper.
Step 2Heat half the oil and half the butter in a skillet. When hot, add the chicken, seasoned side down and cook, over medium-high heat, until browned about 5 minutes. Turn and cook the other side, about 5 minutes. Add the tomato sauce to the pan, lower the heat and simmer 5 minutes or until the chicken is cooked through.
Step 3Meanwhile, in another saute pan, heat the remaining oil and butter and saute the peppers over medium heat until soft and wilted. Turn off heat and set aside.
Step 4Open the beans and heat in a small saucepan. Heat the rice.
Step 5To serve: Split the rice between 4 warmed bowls; top with some of the black beans and a little bean liquid (not a lot, just a little); top with the peppers, sprinkle the cheese on, then cut the chicken into slices and place on top; spoon the remaining sauce on top and top with more cheese, if desired. (if using the pepper jack, put on top of the chicken and then place briefly under the broiler to melt)