Mix broth, vegetables 1 teaspoon parsley and garlic in a large pot. Add 1 cup of water and bring to a boil. Add rice and bring back to a boil. Cover and simmer for 25 minutes. Uncover and simmer for 5 more minutes. Set aside.
While rice cooks, put chicken and broccoli in a mixing bowl. Add the lime juice, parsley, salt, and pepper. Mix well until chicken and broccoli are coated with seasonings. Transfer the chicken and broccoli to a baking pan, spreading it evenly in the bottom with a spatula. Bake for 30-35 minutes.
Remove chicken and broccoli from oven and allow to cool.divide rice into 4 1/2 cup servings. Divide chicken and broccoli into equal portions and place on top of rice.