For the vinaigrette, reduce the cider in a sauté pan over medium heat until 2/3 cup remains. Cool. Place the vinegar, mustard, shallots, and chervil in a bowl. Mix well. Drizzle the oils in slowly. After the dressing has emulsified, add the cider. Season and reserve.
For the crispy beets, fry the sliced beets until crisp. Drain on paper towels, and salt lightly.
For the salad, combine the salad ingredients with half of the vinaigrette in a large metal mixing bowl. Place the bowl over a medium flame. Quickly toss the salad to wilt the greens slightly. Transfer to six plates. Top with the crispy beets. Drizzle the remaining vinaigrette around the salad.