Step 1
Finely chop the smoked salmon and transfer it to a small bowl. Combine with softened butter, mashing the mixture thoroughly using a fork. Incorporate lemon zest and minced dill, ensuring the ingredients are evenly distributed. Shape the mixture into a compact cylinder, approximately two inches in diameter, wrap it in plastic, and place it in the freezer. Preheat four serving plates to keep warm.
Step 2
Heat a large skillet, preferably cast iron, over medium-high heat. Add olive oil and spread it evenly across the pan's surface. Thoroughly dry the salmon fillets using paper towels, then place them skin-side down in the skillet. Raise the heat to high, cooking for about three minutes until the skin is crisp and golden. Flip the fillets and sear the flesh side for an additional two to three minutes, or until the desired doneness is achieved.
Step 3
Retrieve the butter from the freezer and slice it into four evenly sized portions. Once the salmon is cooked, transfer each fillet, skin-side down, to a preheated plate. Lightly season the fish with salt and pepper, then top each portion with a slice of smoked salmon butter. Serve immediately.