1. Blend first 5 ingredients together in blender until smooth, and reserve. If dressing is too thick, whisk in water, 1 tablespoon at a time, to desired consistency.
2. Mix together Parmesan, breadcrumbs, and pepper in shallow bowl. Put eggs in another shallow bowl.
3. Rinse chicken and pat dry. Dip chicken breasts 1 at a time in egg mixture, allowing excess to drip off, then dredge in breadcrumb mixture to coat. Transfer to plate.
4. Heat 3 tablespoons oil in a large non-stick skillet over moderate heat until hot but not smoking. Cook chicken in batches, turning once, until golden brown and cooked through, about 5 minutes total, adding additional oil if necessary.
5. Arrange romaine leaves and chicken on serving plates and drizzle with dressing. Makes 4 servings.