Pat the salmon dry using a paper towel, then season both sides with salt and pepper.

In a large non-stick skillet, heat the olive oil over medium-high heat. Add the salmon fillets and cook for 2 to 3 minutes. Flip them and cook until golden brown, another 2 to 3 minutes. Remove from the skillet and set aside.

Reduce the heat to medium and add the minced garlic and shallot. Sauté gently for about 1 minute. Incorporate the Dijon mustard and add the white wine. Whisk until smooth and cook until the wine reduces by half, approximately 2 minutes.

While whisking, gradually pour in the coconut milk until fully combined, then bring to a rapid simmer.

Once simmering, lower the heat to maintain a gentle simmer. Stir in the lemon zest, lemon juice, chives, dill, tarragon, salt, and pepper. Nestle the salmon back in the sauce and cook uncovered until cooked to your desired doneness, about 3 to 5 more minutes.

Garnish with additional fresh herbs and serve!