Melt the butter in a large skillet, then stir the flour into the melted butter to make a paste. Quickly whisk in the milk to prevent clumps. Let simmer over low heat until thickens. Because we are only adding 2 cups of milk, the sauce will be thick.
Stir in the minced onion, garlic powder, Italian seasoning and salt and pepper. Add the diced chicken breast and let it cook for a few minutes, stirring often. Once the chicken has cooked about halfway through, add the frozen broccoli and combine together.
Add the rice and then pour in the chicken broth. Stir around to get all of the rice kernals into the chicken broth. Bring to bubbling, then reduce heat to low and cover for 18 to 20 minutes, or until rice is tender. Stir only one time during the time the rice is cooking, and do it quickly because you don't want too much liquid escaping from the skillet.
Once the rice is tender, you can stir in the shredded cheese or add it on top of each serving.
Serve Cheesy Chicken, Broccoli & Rice Skillet Dinner right out of the skillet as a one-dish dinner!
Dairy Free Modification: Use rice milk when make the white sauce, omit the cheese...it's still wildly tasteful without it!