Mix the black pepper, olive oil, lemon juice, Worcestershire sauce and 1 teaspoon of salt together in a small bowl.
Cut the chicken into bite size pieces then add them to a large zip-top bag along with the olive oil mixture and toss to combine. Seal and marinade for at least 30 minutes in the fridge, or up to 8 hours.
Add the rice, 1 ¾ cup of chicken broth and the remaining salt to a deep saucepan or a small soup pot and bring it to a boil over medium heat.
Cover and reduce the heat to low medium. Cook for 18-20 minutes. Remove from the heat and let sit for five to six minutes without removing the lid.
While the rice is cooking, preheat the oven to 375 degrees Fahrenheit.
Heat a large frying pan over medium heat and add the chicken along with the marinade sauce. Cook for about 3 minutes on each side, or until the chicken is cooked thru.
Remove from the pan and set aside.
Melt 2 tablespoons of the butter in the pan, add the onion and cook until soft and translucent. Then add the garlic and cook for one minute.
Add 2 more tablespoons of butter to the pan, reduce the heat to low medium and whisk in the flour. Let it bubble for thirty seconds before adding the chicken broth to the pan. Let the broth thicken before stirring in the milk. Let simmer once again until thickened. Whisk the entire time to prevent burning. Remove from the heat and set aside
Add the broccoli florets and the chicken to the frying pan and stir to combine.
Then carefully stir in the rice and cheese, don’t over stir or the rice will start to gum up. Add salt to taste and pour the mixture into a large cast iron skillet or a 9x13 baking dish.
Remove the pan from the heat and stir in the sour cream. Melt the remaining butter in a medium bowl, add the crushed crackers and stir to combine.
Sprinkle the crackers over the casserole in an even layer and bake for 20-25 minutes, or until crackers have darkened a bit in color.
Remove the casserole from the oven and allow it to sit for 5-10 minutes before serving.