Heat oven to 350°F. Line cookie sheet with cooking parchment paper. Place 2 of the loaf pieces on the parchment paper. Wrap and refrigerate remaining 2 for later use.
Press both pieces into flatbreads about 5 inches long and 1/4 inch thick. Brush with olive oil. Sprinkle with 1 1/2 teaspoons each of the dill and parsley. Bake about 10 minutes or until golden brown.
Meanwhile, place remaining 1/2 teaspoon each of dill and parsley and the buttermilk, shallot, tarragon, pepper and vinegar in dressing shaker or jar with tight-fitting cover. Shake until well mixed. Set aside.
Line 2 plates with lettuce. Top with avocado, chicken, snow peas, cucumber, zucchini and tomatoes. Drizzle with dressing.
Allow flatbreads to cool 2 minutes before serving alongside salads.