Peel the turnips, chop into 1/2-inch pieces and add to a 2-quart pot. Peel the potato, quarter it, cut the quarters into 1/2-inch wedges and add to the pot. Cover with cold water, add 1 tablespoon salt and bring to a boil. Reduce the heat, bring to a simmer and cook until the vegetables are tender when pierced with a fork, about 20 minutes.
Strain the vegetables in a colander. Add them to the bowl of a stand mixer fitted with the whisk attachment or use a hand-held mixer and whip until blended. Add the sour cream and mustard and mix on medium speed until the mixture is smooth and creamy. Add salt and pepper to taste.
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