Bring a medium pot of salted water to a boil. Add the broccoli and cook until tender, about 10 minutes. Drain thoroughly.
Put the potatoes in a medium pot, cover with cold water and add 2 tablespoons salt. Bring just to a simmer and cook the potatoes, uncovered, until tender, about 45 minutes. Drain.
Peel the potatoes and return them to the pot (if desired, pass them through a ricer or food mill after peeling). Add the broccoli. Mash the potatoes and broccoli with the milk and butter using a fork or potato masher. Stir in the bacon, 2 teaspoons salt and a few grinds of pepper. Serve sprinkled with more bacon.