Preheat oven to 350°F. Grease an 8×8-inch baking dish.
Heat 1 tablespoon vegetable oil in a large skillet over medium-high heat.
Add 1 pound bite-sized pieces of boneless skinless chicken breast to the skillet. Cook, stirring occasionally, until browned and no longer pink inside, about 5–7 minutes.
Add 2 cups small broccoli florets to the skillet and cook 2–3 minutes more, until broccoli is bright green and just starting to soften.
Pour in 1 cup chicken broth and bring the mixture to a boil.
Stir in 1 1/4 cups instant white rice (uncooked), 8 ounces cream cheese (cut into cubes to help it melt), 2 tablespoons milk, 1 teaspoon Italian seasoning, garlic salt (to taste), and pepper (to taste). Reduce heat to medium-low and stir until the cream cheese is mostly melted and the mixture is well combined, about 2–3 minutes.
Spoon the mixture into the greased 8×8 baking dish and smooth the top.
Evenly sprinkle 1 cup Italian 5-cheese (shredded) over the top. Cover the dish with foil or a lid.
Bake in the preheated 350°F oven for 22–26 minutes, until the rice is tender and the casserole is heated through and bubbly. If desired, remove the cover for the last 2–3 minutes to lightly brown the cheese.
Let the casserole rest 5 minutes before serving.