Make the dressing. In a bowl, whisk mayo, Greek yogurt, anchovy, garlic, lemon juice, Dijon, Parmesan, and black pepper. Add water 1 teaspoon at a time until it’s creamy and pourable.
Taste and adjust salt, pepper, and lemon.
Prep the spice blend. In a small dish, combine smoked paprika, garlic powder, onion powder, oregano, thyme, cayenne, salt, and black pepper.
Season the salmon. Pat the fillets dry. Rub with a little oil, then coat all over with the spice blend, pressing to help it stick.
Heat the pan. Set a large cast-iron or heavy skillet over medium-high heat. Add the remaining oil and let it shimmer.
Good heat equals a flavorful crust.
Sear the salmon. Place fillets in the pan, flesh-side down if using skin-on. Cook 3–4 minutes until a dark crust forms. Flip, add the butter, and baste.
Cook another 2–4 minutes, depending on thickness, until the center is just opaque and flakes easily. Squeeze on a little lemon.
Rest the fish. Transfer to a plate and let it rest 3 minutes. This helps it stay juicy.
If skin-on, you can leave it or peel it off now—it should release easily.
Toss the salad base. In a large bowl, combine romaine, tomatoes, cucumber, and red onion. Add enough Caesar dressing to lightly coat and toss well.
Build the bowls. Divide the salad among bowls. Top with croutons or toasted breadcrumbs and extra Parmesan.
Add warm salmon on top. Finish with a final drizzle of dressing and a squeeze of lemon.
Serve. Crack a little fresh black pepper over everything. Eat right away while the salmon is still warm and the lettuce stays crisp.