How to Make It
Combine beets, shallot, vinegar, 3 tablespoons of the oil, and ¼ teaspoon each kosher salt and pepper in a large bowl. Set aside to marinate, tossing once.
Combine yogurt, horseradish, and remaining 1 tablespoon oil in a medium bowl. Season with remaining ¾ teaspoon salt and ¼ teaspoon pepper.
Divide yogurt among toasts. Top with marinated beets, radishes, and chives. Drizzle some of the remaining marinade overtop.