In a 10- to 12-inch nonstick frying pan over high heat, boil beets, onion, vinegar, broth, liqueur, sugar, and orange peel, stirring often, until liquid is reduced to 2 tablespoons, 7 to 10 minutes. Let cool to room temperature, or chill airtight up to 1 day.
Stir pomegranate seeds and salt to taste into the beet mixture.
Mound mâche equally on salad plates. Spoon pomegranate and beet mixture alongside greens. Sprinkle feta cheese over greens.