Peel the horseradish root with a vegetable peeler. Grate finely or whirl in a food processor until finely chopped. In a small bowl, mix horseradish with vinegar.
In another bowl, whisk crème fraîche until slightly thickened. Stir in horseradish mixture, parsley, and salt and pepper to taste.
* Fresh horseradish is sold in well-stocked produce markets; if you can't find it, you can substitute 1/4 to 1/2 cup prepared horseradish and omit the vinegar. Either way, make the sauce a day ahead of time to allow the flavors to blend.
Make ahead: 1 day; keep chilled.
Note: Nutritional analysis is per tbsp.