Cook onion, chopped bell pepper, mushrooms, and garlic in 1/4 cup of butter until the onion is transparent. Add rice and herb packets and cook, stirring, until the rice begins to turn golden.
Add the chicken broth and simmer gently in a covered pan until the rice is barely tender and the liquid is mostly absorbed.
Preheat oven to 400 degrees.
Butter a deep casserole dish. Lightly transfer half the rice mixture to the dish with a fork. Top with half the pepper rings and half the cheese. Repeat layers. Dot with remaining butter and pour cream over the top.