Process anchovies and garlic in a food processor until minced. Add yogurt, mayo, lemon juice, Worcestershire, and mustard. Process until smooth; salt and pepper to taste. (Makes 2/3 cup.)
Place each chicken breast between two waxed paper sheets. Gently pound with a mallet until evenly 1/2-inch thick. Brush both sides with oil and season with salt and pepper.
In a large skillet over medium-high heat, sauté chicken 3 minutes per side, or until just cooked through.
Place chopped romaine in a large salad bowl. Add three-fourths of dressing, croutons, and half of cheese; toss to mix. Divide salad among six plates. Cut chicken into thin slices. Divide among salads and top with any cooking juices. Sprinkle with remaining Parmesan cheese and serve with additional dressing on the side.