Season both sides of the salmon fillets liberally with salt & pepper.
Place the olive oil in a medium pan over a medium-high flame. Once the oil starts to smoke slightly, add your salmon fillets and sear on each side until crisp and lightly brown, about 1-2 minutes per side.
Once the salmon is almost cooked through, add the butter, half of the lemon juice, and parsley. Baste the salmon with a spoon. Pull salmon off the heat once cooked through.
Meanwhile, place the arugula or spring greens in a bowl and use the remaining half of the lemon juice, 2 TBSP of olive oil, and a pinch of salt to make a light dressing.
To serve, place the dressed spring greens / arugula in a plate and top with the seared salmon.