Spray the bottom and sides of a 13×9 baking dish with cooking spray; set aside.
In a large bowl, whisk together milk, cheddar soups and 3/4 teaspoon salt until smooth. Set aside one cup (not more) of the soup mixture. To the remaining soup mixture, stir in uncooked rice then pour mixture into prepared baking dish.
Cut chicken breasts into 1-inch pieces then season with salt, pepper and garlic. Arrange chicken pieces on top of rice mixture.
Arrange broccoli florets on top of the chicken.
Pour reserved soup mixture evenly over broccoli. Cover dish very tightly with aluminum foil and bake at 350 degrees for 1 hour and 15 minutes. Consider covering with a double layer of foil to ensure a tight fit – we need all the steam to stay in the dish to ensure everything cooks properly.
Combine crushed crackers, melted butter and garlic and mix well. Remove casserole from oven, remove aluminum foil then sprinkle cracker topping evenly over casserole. Continue baking, uncovered, for 15 minutes.
Remove from oven and let rest for at least 15 minutes then serve. Don’t skip this step – it’s needed for the rice to continue cooking and the casserole to set up properly.