Cook and chop the chicken. Cut the broccoli into 2-inch pieces and cook in boiling water until tender; drain. Cook the rice according to package directions. Meanwhile, melt the butter in a pan; blend in the flour. Add the chicken broth and bouillon cube and stir until thick. Stir in the cream, pepper, Parmesan cheese, and 1 cup of the cheddar cheese. Remove from heat. Preheat the oven to 350. In a 9×13 dish, layer the rice, broccoli, chicken, and sauce. Then sprinkle the remaining cup of cheddar cheese on top. Bake at 350 for 20-30 minutes, or until heated through.