Season chicken breasts with salt and pepper and grill over medium-high heat for 6-7 minutes per side until the internal temperature reaches 165°F (74°C).
Allow chicken to rest for 5 minutes before slicing into 1/2-inch strips.
In a small mixing bowl, combine Greek yogurt, lemon juice, Dijon mustard, minced garlic, anchovy paste, and black pepper; whisk until smooth.
In a large chilled bowl, toss the chopped Romaine lettuce with the prepared Greek yogurt dressing until leaves are thoroughly coated.
Divide the dressed lettuce between two plates.
Arrange the sliced grilled chicken and sliced hard-boiled eggs over the lettuce.
Garnish with shaved Parmesan cheese and whole grain croutons before serving.