Fill a large pot with enough water to come 2 inches up the sides of the pot. Set a steamer rack in the pot, cover, and bring the water to a boil over high heat. Add the potato chunks and cook until they are very tender, about 18 minutes. Transfer the potatoes to a medium bowl and mash until smooth.
Place broccoli into steamer rack and steam over medium heat until the broccoli is very tender, about 12 minutes. Transfer the broccoli to the bowl of a food processor. Add the broth, cream cheese, and Parmesan. Process until the broccoli is pureed and almost smooth.
Stir the broccoli puree into the mashed potato and blend well. Season the puree to taste with salt and pepper, and serve.