Preheat the grill to medium-high heat.
Season the salmon fillets with salt, pepper, and drizzle with olive oil.
Grill the salmon fillets for about 4-5 minutes per side, or until cooked to your desired doneness.
In a small saucepan, melt the butter over medium heat.
Stir in the lemon juice and chopped parsley into the melted butter.
Simmer the sauce for 1-2 minutes, then remove from heat.
Pour the lemon butter sauce over the grilled salmon fillets before serving.
Serve immediately, garnished with additional chopped parsley if desired.