Preheat oven to 350 F. Place Arctic Char fillets on tray and cover with foil. Place fillets in oven until hot all the way through (approximately 10 minutes). Heat 1 teaspoon vegetable oil in a pan, add diced shallots and cook until translucent. Add cup of wine and let reduce by half, then add cream and let reduce till it thickens slightly; set aside. Slice mushrooms and saute in 1 teaspoon of butter in a skillet until golden. Add angel hair pasta to boiling, salted water. Cook till al dente then drain and set aside.
Toss angel hair pasta with heated cream sauce; add mushrooms and chopped herbs. Twirl the pasta on a serving fork and slide onto a plate. Fan slices of Arctic Char fillet on top. Drizzle remaining sauce over fish. Garnish with blanched asparagus spears.