Add an inch of water to the bottom of a 4-quart pot, and place a steamer basket in the bottom. Add the potatoes and bring the water to a boil; cover and steam for 10 minutes.
Add the broccoli florets and steam 5 more minutes, or until the potatoes are quite tender, and the broccoli is tender enough to pierce easily with a fork.
Transfer the vegetables to a large mixing bowl. Add butter, milk, cheese, pepper and salt. Using a hand mixer, blend until smooth.