Season chicken breasts with olive oil, salt, and black pepper.
Grill or pan-sear chicken over medium-high heat for 6 minutes per side until the internal temperature reaches 165°F (74°C).
Allow chicken to rest for 5 minutes before slicing into 0.5-inch strips to preserve juices.
In a small mixing bowl, whisk together Greek yogurt, lemon juice, Dijon mustard, Worcestershire sauce, minced garlic, and mashed anchovies until smooth.
Place chopped romaine lettuce in a large salad bowl and toss with approximately half of the prepared dressing to coat evenly.
Distribute the dressed lettuce into two serving bowls.
Top with sliced chicken, shaved Parmesan cheese, and whole grain croutons.
Drizzle the remaining dressing over the salads and serve immediately.