Preheat your grill to medium heat, about 350°F (175°C). Rub vegetable oil on the grill to prevent sticking.
Season both sides of the salmon filets with blackening seasoning.
Place the salmon filets on the preheated skillet and cook for 3-4 minutes on each side, or until the salmon is cooked to your desired level of doneness. Remove from the grill and set aside.
In a food processor, add the anchovies, egg yolk, garlic and lemon juice. Pulse until smooth and creamy. Add in the dijon mustard, olive oil and parmesan cheese. Continue to pulse until smooth.
In a large mixing bowl, combine the lettuce, Caesar dressing, shaved Parmesan cheese and croutons. Toss until the lettuce is evenly coated with the dressing.
Divide the salad among serving plates.
Place a blackened salmon filet on top of each salad.
Serve the salad immediately with lemon wedges on the side.