Pat the salmon fillets dry with paper towels and brush both sides with olive oil. Season generously with salt and pepper.
In a mixing bowl, combine Dijon mustard, heavy cream, lemon juice, minced garlic, and chopped dill. Whisk until smooth.
Place the salmon fillets in a shallow dish and pour half of the creamy Dijon sauce over them. Let them marinate for 15-20 minutes.
Preheat your grill to medium-high heat. Ensure that the grill grate is clean and lightly oiled.
Place the salmon fillets skin-side down on the grill and cook undisturbed for about 4-5 minutes. Flip gently and grill for an additional 3-4 minutes until cooked through.
Remove the salmon from the grill and drizzle with the remaining creamy Dijon sauce over each fillet. Garnish with extra fresh dill before serving warm.