In a bowl, mix broth, olive oil, vinegar, capers, lemon juice, shallots, and mustard. If desired, cut hearts of palm in half lengthwise. Lay hearts of palm in dressing, turn over, and let stand at least 5 minutes.
Separate egg yolks from whites. Chop both or finely mash with a fork; keep separate.
Lift hearts of palm from dressing and arrange on salad plates. Add parsley and shrimp to dressing in bowl and mix. Pit, peel, and thinly slice avocado; arrange on salads. Spoon shrimp and all the dressing over the hearts of palm and avocado. Sprinkle with egg whites, then yolks. Add salt and pepper to taste.