Prepare the marinade: In a small bowl, whisk together the olive oil, lemon juice, minced garlic, chopped parsley, Dijon mustard, salt, and pepper. Taste and adjust seasoning as needed—add more lemon for tang or extra garlic for flavor.
- Marinate the salmon: Place the salmon fillets in a shallow dish or resealable plastic bag. Pour the marinade over the salmon and toss to coat. Let the salmon marinate for at least 15-20 minutes (or up to 1 hour if you have time) in the refrigerator.
- Preheat the grill: Preheat your grill to medium-high heat. If using a grill pan, heat it over medium-high heat on the stove.
- Grill the salmon: Place the salmon fillets on the grill, skin-side down if they have skin. Grill for 4-5 minutes per side, depending on the thickness of the fillets. The salmon is done when it flakes easily with a fork and has reached an internal temperature of 145°F (63°C). If you like your salmon with a bit of char, you can grill it for an additional minute or two on each side.
- Serve: Remove the salmon from the grill and let it rest for a few minutes. Serve with lemon wedges and garnish with fresh herbs, if desired.