Preheat the oven to 400°F. Scrub the beets clean, leaving the skins on, and wrap each one individually in aluminum foil.
Place the foil-wrapped beets on a rimmed baking sheet and roast for 45–60 minutes, until a fork slides into the center with almost no resistance.
Let the beets cool in the foil for at least 20 minutes, then unwrap and rub the skins off under running water. Cut into ½-inch cubes.
Combine the champagne vinegar, olive oil, honey, dijon mustard, minced shallot, salt, and pepper in a jar with a tight lid. Shake vigorously for 20 seconds until slightly thickened.
Julienne the jicama, segment the oranges, and thinly slice the red onion. Soak the onion in ice water for 10 minutes, then drain well.
Spread the arugula across a platter or individual plates. Scatter the beets, jicama, orange segments, and drained onion over the top.
Drizzle with about two-thirds of the vinaigrette, adding more to taste. Finish with crumbled goat cheese and candied walnuts. Serve immediately.