01 - Preheat oven to 400°F. Line a baking sheet with parchment paper.
02 - Pat the salmon fillet dry with paper towels. Rub with olive oil, then coat evenly with smoked paprika, sea salt, and black pepper.
03 - Place the seasoned salmon on the prepared baking sheet and bake for 12 to 15 minutes, until just cooked through and the flesh flakes easily with a fork. Remove from the oven and let rest until cool enough to handle.
04 - While the salmon bakes, whisk together mayonnaise, Greek yogurt, chopped anchovy fillets, minced garlic, lemon juice, Dijon mustard, Worcestershire sauce, and grated Parmesan in a mixing bowl. Season with salt and pepper to taste. Adjust any seasoning as desired.
05 - In a large salad bowl, combine the torn romaine lettuce, halved cherry tomatoes, and sliced red onion. Drizzle with about two-thirds of the Caesar dressing and toss to coat evenly.
06 - Flake the cooled salmon into large, bite-sized pieces. Arrange the salmon over the dressed salad, then top with shaved Parmesan cheese and croutons. Drizzle with the remaining dressing and serve immediately.