Bring 1 inch of water to a boil in a large pot. Place potatoes in a steamer basket and steam for 10 minutes. Place broccoli on top, cover and steam until the potatoes and broccoli are tender, 6 to 8 minutes more.
Transfer the broccoli to a large bowl and coarsely mash with a potato masher. Add the potatoes, cheese, milk, salt and pepper and continue mashing to desired consistency.