Place the well-scrubbed potatoes in a large dairy pot and fill with cold water to 1 inch above the potatoes. Bring to a boil and stir in 1 tablespoon of salt.

Cook uncovered for 30 to 40 minutes. Add the broccoli and cook for an additional 5 to 10 minutes, or until a knife pierces through the potatoes.

Drain the potatoes and broccoli in a colander and peel the potatoes. Return the potatoes and broccoli to the pot and mash them using a masher.

Stir in the cheese, butter, and milk, and whisk until melted. Season with salt and pepper to taste. Serve warm.