Prep the Salmon: Remove salmon fillets from the refrigerator 10 minutes before cooking. Pat the surfaces completely dry on all sides with paper towels. Season all sides evenly with sea salt, black pepper, and optional garlic powder.
Sear the Fillets: Set a large cast iron skillet or heavy stainless steel pan over medium-high heat. Add the extra virgin olive oil and 1 tablespoon of butter. When the pan is hot and the fats are shimmering, lay the salmon flesh-side down. Sear undisturbed for 4 to 5 minutes until a deep, caramelized crust forms. Carefully flip the fillets using a fish spatula.
Build the Sauce: Lower the pan heat to medium. Drop the remaining 2 tablespoons of cold butter and the minced fresh garlic into the open spaces of the skillet. Cook the garlic for 1 minute until fragrant, ensuring it does not scorch.
Baste to Finish: Pour the fresh lemon juice and chopped parsley directly into the bubbling butter. Tilt the skillet slightly to pool the juices and use a large spoon to continuously pour the hot garlic-lemon butter over the tops of the salmon fillets for an additional 2 to 3 minutes until the fish flakes easily.
Plate and Serve: Transfer the salmon to a clean serving platter. Pour all remaining pan sauce over the fish, garnish with extra fresh parsley, and serve immediately alongside fresh lemon wedges.