Combine the mayo, Parmesan cheese, garlic, Dijon mustard, fish sauce, Worcestershire sauce, lemon juice, olive oil, salt, and pepper in a blender or food processor. Blend until smooth. Transfer the dressing to a container and refrigerate for at least 15 minutes.
Mix the salt, pepper, onion powder, garlic powder, and paprika in a small bowl, then sprinkle the spice mixture evenly over both sides of the chicken.
Heat some olive oil in a skillet over medium-high heat. Cook the chicken for 6-7 minutes on each side until the chicken is fully cooked. Cover it with a lid to help cook evenly. Remove the chicken from the heat and let it rest.
Place the chopped romaine lettuce, croutons, and 1/2 cup of the grated Parmesan cheese in a bowl. in a large bowl. Drizzle 1/4 to 1/2 cup of the prepared homemade dressing and toss gently to coat the salad evenly.
Slice the chicken into thin slices, place it on top of the salad, and sprinkle additional Parmesan cheese over top of everything. Serve with the remaining creamy dressing and lemon slices or wedges on the side.