Prepare the horseradish root: Start by peeling the horseradish root using a vegetable peeler. Once peeled, chop the root into smaller pieces that are easier to handle.
Grate the horseradish: Grate the horseradish root into fine shreds using a microplane or a small food processor.
Combine the grated horseradish and vinegar: Mix the grated horseradish with a small amount of vinegar. The vinegar will help preserve the color and flavor of the horseradish while also mellowing its intensity. Stir the mixture well to ensure the horseradish is evenly coated.
Let the mixture sit: Allow the horseradish and vinegar mixture to sit for about 10 minutes. This resting period will allow the flavors to meld together and soften the sharpness of the horseradish. You are essentially making your own prepared horseradish.
Add the remaining ingredients: After resting, stir in the Dijon mustard, sour cream, and heavy cream.
Fold in the minced chives: Mince the fresh chives and fold them into the horseradish cream.
Season with salt and pepper: Taste the sauce and adjust the flavor by adding a pinch of salt. The salt will enhance the overall taste. Stir well to incorporate the seasonings.
Refrigerate and let the flavors meld: Transfer the sauce to an airtight container and refrigerate for at least an hour before serving.