Place scallion, oil, and horseradish sauce in a blender. Puree until smooth and transfer to a bowl; salt to taste. Set aside.

Place potatoes and parsnips in a 4-quart pot, cover with cold water by 2 inches and bring to a boil over moderately high heat; add salt. Simmer until vegetables are very tender, about 25 minutes. Reserve 1/2 cup cooking liquid and drain in a colander. Return vegetables to pot; add milk, butter, and 1/4 cup cooking liquid. Mash with a handheld potato masher until smooth, adding enough of remaining 1/4 cup cooking liquid to reach desired consistency. Fold in scallion puree; salt and pepper to taste. Transfer to a serving bowl and garnish with snipped scallion, if desired. Makes 8 servings.