Prepare the Garlic and Anchovy Paste: On a cutting board, finely mince the garlic and anchovy fillets. Add the salt and, using the flat side of your knife, mash them into a smooth paste. Transfer the mixture to a small bowl.
Make the Caesar Dressing: Add the mayonnaise, Dijon mustard, lemon juice, black pepper, olive oil, and parmesan cheese to the bowl. Whisk until the dressing is smooth and creamy.
Season the Chicken: Pat the chicken thighs dry and season them with the salt.
Marinate the Chicken: Coat the chicken thighs evenly with ½ cup of the Caesar dressing. Let them marinate for 1 hour.
Preheat the Broiler: Preheat the broiler.
Broil the Chicken: Place the chicken thighs on a broiler-safe pan and broil them for 10 to 14 minutes, until they reach an internal temperature of 175°F.
Rest and Serve: Remove the chicken from the oven and let it rest for 10 minutes before serving.