In a large mixing bowl, combine the minced garlic, finely grated Parmesan cheese, mayonnaise, and minced anchovies. Squeeze the juice of half a lemon into the bowl, whisking everything together until smooth and creamy. Taste it, and adjust the seasoning if necessary.
Heat your grill or skillet over medium-high heat. Season the salmon fillets with salt and pepper. Place the salmon skin-side down on the grill or in the skillet, cooking for about 4-6 minutes per side depending on thickness. A meat thermometer should read 145°F when it's fully cooked.
While the salmon is cooking, roughly chop or tear the romaine lettuce into bite-sized pieces. Place it in a large mixing bowl. Add the Caesar dressing to the romaine and toss until the leaves are well coated.
Once the salmon is cooked, allow it to rest for a few minutes. Then, flake the salmon into large chunks and gently place it on top of the dressed romaine.
Finish the salad by squeezing the remaining lemon half over the top for a fresh burst of flavor. Serve immediately and enjoy!
