Place chicken in crockpot. Sprinkle with dressing mix. Slice mushrooms and dice onion; add to crockpot. Using a medium sized bowl, mix cream of chicken soup with 1/4 cup broth; whisk together. Pour into crockpot. Cook on low for 3 hours.
Once chicken has cooked for 3 hours, add broccoli and continue to cook on low for an additional hour.