Place the potatoes into a large pot and cover with salted water. Bring to a boil over high heat, then reduce heat to medium-low, cover, and simmer until tender, about 20 minutes. Drain and allow to steam dry for a minute or two. Mash potatoes in a large bowl with the butter and milk, and season with salt and pepper.
Whip the potatoes using an electric mixer set on medium until smooth, 3 to 4 minutes, adding more milk if the potatoes are too dry. Beat in the whole grain mustard, and serve immediately.
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