Make the dressing: combine 1/2 cup plain Greek yogurt, 2 tablespoons grated Parmesan, 2 tablespoons olive oil, juice of 1 lemon, 1 teaspoon Dijon mustard, 1 peeled garlic clove, and the optional anchovy filet in a blender and pulse until smooth.
Toss the salad: place the chopped romaine and 2 ounces shaved Parmesan in a large bowl and toss with the dressing until evenly coated; set aside.
Prepare the salmon seasoning: in a small bowl, mix 2 teaspoons freshly ground black pepper, 3/4 teaspoon sea salt, and 2 teaspoons lemon zest.
Season the salmon: pat the salmon fillets dry and rub them evenly with the lemon-pepper seasoning.
Heat the skillet: place a heavy cast iron or stainless steel skillet over medium-high heat and heat for 3–4 minutes until very hot.
Add oil and cook the salmon: add 2 tablespoons olive oil to the hot skillet. When the oil shimmers, add 1–2 fillets at a time without crowding. Cook until the fish releases easily from the pan, about 3–5 minutes per side depending on thickness. Flip and cook until well-browned on both sides and the salmon flakes with a fork. Repeat with remaining fillets.
Assemble and serve: divide the dressed romaine among plates, top with lemon pepper salmon fillets, and serve immediately.