Place the mayonnaise, grated Parmesan, lemon juice, Dijon mustard, minced garlic, halal-certified Worcestershire-style sauce, salt, and black pepper in a small bowl.
Whisk until smooth and creamy. Set the Caesar-style sauce aside while you prepare the chicken.
Pat the chicken breasts thoroughly dry with paper towels. If they're particularly thick, gently pound them to a more even thickness so they cook consistently.
Lightly season both sides of the chicken with salt and freshly ground black pepper.
Heat the olive oil in a large skillet over medium heat until shimmering.
Add the chicken breasts, leaving enough room between them for proper browning.
Cook for approximately 6–7 minutes on the first side without moving them excessively. Flip and continue cooking for another 5–7 minutes, depending on thickness.
Check the thickest part of each chicken breast with an instant-read thermometer. The chicken should reach a safe internal temperature of 165°F (74°C).
Reduce the heat to low. Spoon some of the prepared Caesar sauce over each chicken breast.
Cover the skillet and warm gently for about 2 minutes. Avoid boiling the sauce, which can cause it to separate.
Remove the Melt In Your Mouth Caesar Chicken from the heat and allow it to rest briefly.
Spoon additional Caesar sauce over each serving as desired.
Finish with fresh chopped parsley and Parmesan shavings. Serve immediately with your favorite side dishes.