Season fillets with salt and pepper, to taste. Spread one teaspoon of mustard on flesh side and pat ¼ cup of the herb mixture on top of mustard, on each fillet.
Heat a large cast-iron frying pan over high heat until sprinkled water jumps off the pan. Cook salmon fillets, flesh and herb side down, for a couple minutes (2-3 depending on how hot your pan is), until nicely browned.
Turn fillets over, remove pan from heat and add white wine to the pan. Do not pour liquid over fillets, as you will wash off the mustard crust. Place pan into preheated oven and bake for about 5-10 minutes, or until flesh will pull apart easily with a fork.
Chef's notes: Fines herbes are a combination of finely chopped fresh herbs. For delicately flavored fish like salmon, try to use a mixture of chervil, tarragon, parsley and a pinch of thyme. You can use crushed, dried herbs if fresh herbs are not available. When substituting dried herbs for fresh, use about 1/3 the amount, as dried herbs are much more potent. Conversely, when substituting fresh herbs for dried in a recipe, use about three times as much. You may use broth or water in place of white wine.