Pat the salmon fillets dry with paper towels. This helps to achieve a crispy skin when frying.

Season both sides of the salmon fillets with salt and black pepper, ensuring even coverage.

In a large skillet, heat the olive oil over medium-high heat until shimmering. This indicates that the oil is hot enough to sear the salmon.

Carefully place the salmon fillets skin-side down in the hot skillet. Avoid overcrowding the pan; cook in batches if necessary.

Cook for about 4-5 minutes without moving them. This allows the skin to become crispy.

Using a fish turner, gently flip the fillets and cook for an additional 3-4 minutes, or until the salmon is cooked through and flakes easily with a fork. The internal temperature should reach 145°F (63°C).

In the same skillet, reduce the heat to low and add the butter. Allow it to melt, scraping up any browned bits from the bottom of the pan.

Stir in the lemon juice and mix well. This adds a bright flavor to the sauce.

Remove from heat and set aside.

Plate the salmon fillets and drizzle the lemon butter sauce over the top.

Garnish with chopped parsley for a fresh touch.