Remove salmon filets from the refrigerator and let sit at room temperature for 15 minutes if time allows.
Pat the filets dry using a paper towel. Season both sides generously with salt and pepper to taste. Don’t skimp on the seasoning here!
Heat a large cast-iron skillet over medium high heat. Once hot, drizzle with the olive oil. Add the filets, skin side down and cook for about 3-4 minutes. Do not disturb the salmon while cooking.
Reduce heat to medium. Carefully flip the filets over with a flat spatula. Add the butter, lemon slices and rosemary sprigs in between the filets. Cook for another 3-4 minutes, basting with the lemon herb butter. Salmon is done when it’s opaque in color.
Remove pan from burner and let salmon rest for 2-3 minutes before plating. Drizzle with the pan juices and serve with additional lemon slices if desired.