Peel and cut potatoes in 1 1/2 inch pieces and place in a pot of cool salted water. Water should cover the potatoes by two inches to have room for the broccoli. Place pot on medium-high heat.
Meanwhile, cut broccoli into florets. Once the water comes to a boil reduce heat to maintain a medium-low boil and cook potatoes for 12 minutes.
Add broccoli to the pot and continue to cook the potatoes and broccoli for another 10 minutes. When a fork can easily pierce the stem they are ready to mash.
Drain the water and mash with butter, milk, and salt.