Rinse the salmon fillets and pat until they are completely dry. Using the back of your knife, scrape any excess moisture from the skin of the salmon.
Mix the herbs and garlic in a bowl.
Brush the flesh of both salmon fillets with Dijon mustard and season with salt and pepper.
Place the salmon flesh side down in the garlic herb mixture and press to coat.
Heat the oil in a skillet. Add salmon skin side down. Cook for three minutes or until skin has browned and crisped up. Add more oil as desired.
Add butter, and as it melts, spoon over top of the salmon.
Flip the salmon and cook for about another three minutes, or until cooked to desired doneness.
Remove salmon to a plate.
Drain the butter from the pan used to cook the salmon. Over medium heat, add heavy cream to the pan, swirling it gently so that it won’t separate. Add fresh lemon juice, a dollop of mascarpone, and whisk. Add a pinch of salt. Reduce for about 45 seconds.
Plate the salmon on top of the mascarpone sauce, and garnish with dill and parsley. Finish with a squeeze of lemon juice and a drizzle of olive oil.