Preheat oven to 350°F. Spray a 9x13-inch casserole dish with cooking spray. Set aside.
Rinse the frozen broccoli under cold water to slightly thaw. Do not worry if the broccoli is not fully thawed by the time you need to add it to the casserole.
Heat the olive oil or butter in a nonstick skillet over medium heat. Add the onion; cook for 3-5 minutes, until softened. Add the garlic and cook for 1 more minute. Remove from the heat and transfer to a large mixing bowl.
Add the broccoli, chicken, rice, soups, cheese, chicken stock, and milk. Stir to combine. Season with a heavy pinch of salt and pepper and mix thoroughly.
Pour the mixture into the prepared casserole dish and top evenly with the crushed crackers.
Bake for 30-40 minutes or until the rice is cooked through, the edges are bubbling, and the crackers are golden brown.
