How to Make It
Preheat the oven to 375°. On a large sheet of heavy-duty foil, toss the beets with oil and season with salt and pepper. Wrap the beets in the foil and bake for about 1 hour, until tender when pierced. Let the beets cool slightly, then peel and let cool completely. Slice the beets crosswise 1/8 inch thick.
Meanwhile, in a small saucepan, combine 1/3 cup of water with the balsamic vinegar, mustard seeds, sugar and a pinch of salt and bring to a boil. Simmer over moderately low heat, stirring occasionally, until the seeds are nearly tender and most of the liquid is absorbed, about 12 minutes; let cool.
In a small bowl, whisk the tarragon vinegar with the Dijon mustard, horseradish and 3 tablespoons of olive oil. Season the vinaigrette with salt and pepper.
Arrange the beet slices on 4 plates or a platter, season with salt and pepper and drizzle with the horseradish dressing. Dollop the pickled mustard seeds on top; if the pickling liquid seems too thick, stir in water 1 teaspoon at a time before dolloping. Garnish the beets with arugula leaves, snipped chives and minced red onion and serve.