Place the prepared horseradish in a fine-mesh strainer over a bowl. Press down gently with a spoon to extract and discard excess liquid, ensuring a thick final sauce.

In a medium mixing bowl, combine the drained horseradish, sour cream, Dijon mustard, and apple cider vinegar. Whisk vigorously until the mixture achieves a glossy, smooth texture with visible pale yellow mustard flecks.

Gently fold in half of the chopped fresh green chives, the coarse black pepper flakes, and kosher salt. Stir with a spatula just until combined to prevent the green color from bleeding into the off-white base.

Transfer to a small ceramic serving bowl, cover tightly, and refrigerate for at least one hour to allow flavors to meld. Before serving, generously garnish the top with the remaining fresh green chives and extra cracked coarse black pepper.