Bring one 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.
Tender the broccoli to a large bowl and coarsely mash with a potato masher.
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.