Step 1

Press salmon filets between paper towels to dry surfaces thoroughly. Season on all sides with salt and pepper. Heat 1/3 cup oil in a large stainless steel skillet over medium-high heat until shimmering. Add salmon filets skin side-down. Immediately reduce heat to medium-low. Cook, pressing gently on back of filets to ensure good contact with skin, until skin is rendered and crisp, about 6 minutes. If skin shows resistance when attempting to lift with a spatula, allow it to continue to cook until it lifts easily.

Step 2

Meanwhile, in a large bowl, combine arugula, lemon juice, remaining 3 tablespoons olive oil, and avocado. Season with salt and pepper and toss in grated cheese.

Step 3

Flip salmon and cook on second side until a thermometer inserted into the thickest part registers 120°F for medium rare or 130°F for medium, about 1 minute longer. Transfer salmon to a paper towel-lined plate. Spoon salad onto plates, top with salmon, and serve.