In a blender, add balsamic vinegar and next 7 ingredients. Process for 5 seconds. Keep motor running and add oil in a thin stream until emulsified to make dressing/marinade.
Place duck breasts in a bowl and toss with some of the marinade.
Cover and refrigerate for at least 1 hour and up to 12 hours. Remove duck breasts from marinade and broil, grill or pan-sear until medium-rare.
Allow to rest for several minutes before slicing thinly across the grain.
In a large bowl, combine remaining ingredients and toss with enough dressing to lightly coat contents of bowl.
Mound salad on plates and top with sliced duck. Drizzle additional dressing over duck and serve.