Place chicken broth and butter in a medium saucepan over high heat. Once boiling, add rice and turn down heat to a simmer. Allow to simmer for 40 – 45 minutes until liquid has evaporated. Season lightly with salt and pepper.
When rice has 10 minutes left to cook, start your chicken. Place olive oil in a large skillet set to medium-high heat. When oil is hot, add the chicken.
Once chicken has begun to cook on the outside, but is still pink inside, sprinkle the dressing mix and ½ cup parmesan cheese directly onto the chicken. Toss to coat and continue cooking chicken for about 1 minute.
Add ¼ cup vinegar to help loosen things up a bit. Scrape up any brown bits from the bottom of the pan with a wooden spoon and stir chicken constantly. Once liquid has evaporated, add the additional 2 Tbsp of vinegar and continuously toss again. By now, the chicken should be fully cooked and you should have released all the browned bits from the bottom of the pan. Turn down heat to a simmer to keep things warm.
Steam broccoli in its bag according to package instructions. When done, dump entire contents into the skillet with the chicken. Toss to coat.
When rice is done, dump that into the same skillet and toss. Add remaining ¼ cup cheese and toss until evenly coated.
Divide mixture into 1/4s and plate. Serve with an additional sprinkle of cheese, if desired.