Prep the chicken: Pat chicken dry and season both sides with salt, pepper, and lemon zest. Let it sit for 10 minutes at room temperature.
Cook the chicken: Heat 2 tablespoons olive oil in a skillet over medium-high.
Sear chicken 5–6 minutes per side, until golden and the internal temperature reaches 165°F (74°C). Rest for 5–10 minutes, then slice or dice.
Make the dressing: In a bowl, whisk Greek yogurt, mayonnaise, lemon juice, Dijon, Worcestershire, anchovy paste, and garlic. Stir in 1/4 cup Parmesan and 1 tablespoon olive oil.
Thin with water or milk until creamy and pourable. Season with pepper and a pinch of salt if needed.
Prep the base: Chop romaine into bite-size pieces. Rinse and dry well so the dressing clings.
Assemble bowls: Divide romaine among bowls.
Add sliced chicken, tomatoes, avocado, and croutons. Sprinkle with remaining Parmesan.
Dress and toss: Drizzle dressing over each bowl right before eating. Toss gently to coat.
Finish with a squeeze of lemon and extra pepper.
Adjust to taste: Add more dressing for creaminess, extra Parmesan for savoriness, or a pinch of salt if your croutons are low-sodium.