In a preheated sauté pan, add enough sesame oil to coat the bottom, Sauté garlic, shallots and ginger with the shiitake mushrooms, then add white wine, salt and pepper. Cook ingredients until mushrooms are tender. Remove from heat, mix in parsley and leave mixture in a small bowl to cool. Set aside.
In a preheated sauté pan, add enough sesame oil to coat bottom of pan. Add the fillets and lightly brown each side of the fillet, taking care not cook them. Remove from heat and place fillets onto a baking sheet.
With a pastry brush, coat each fillet with honey mustard, then take the mushroom mixture and gently press an even amount of the mixture on top of each Artic Char fillet.
Cook the Artic Char fillets in a preheated 350 F (180 C) oven for approximately 10 -12 minutes (Artic Char texture should flake lightly with fork).