Preheat oven to 400°F. Wrap each beet in foil; place on a large baking sheet. Roast until tender and easily pierced with a knife, 1 hour to 1 hour and 15 minutes. Carefully unwrap the beets and let stand until cool enough to handle, about 15 minutes.
Meanwhile, whisk ¼ cup oil, 1 teaspoon lemon zest, 2 tablespoons lemon juice, 1 teaspoon ginger, ¾ teaspoon salt, ½ teaspoon mustard, ½ teaspoon honey and ¼ teaspoon pepper in a large bowl until combined. Set aside at room temperature until ready to use.
When the beets are cool enough to handle, remove and discard the skins, using paper towels to wipe the skins off. Cut into ½-inch cubes; add to the bowl with the vinaigrette.
Add chopped shallot to the bowl with the beets and vinaigrette; toss well to coat. Serve at room temperature or chilled. Sprinkle with 2 teaspoons chives before serving.
