Place a large frying pan, preferably cast iron, over medium-high heat. When the pan is hot, add the remaining 3 Tbsp. olive oil and swirl to coat the bottom of the pan. Add the salmon fillets, skin-side down, then press down on each fillet with the back of a metal spatula to maximize the contact with the surface of the pan. (This helps crisp the skin.) Cook on one side, without disturbing, until the skin is crisp and browned, about 4 min¬utes. Add the remaining 1 Tbsp. butter to the pan and swirl it around the fillets. Turn the fillets skin-side up and cook until the salmon is almost opaque throughout but still very moist, or an instant-read thermometer inserted into the center registers 115° to 120°F [45° to 49°C], about 3 minutes longer.