Preheat oven to 400 ˚F (200 ˚C).
In a food processor, mince mushrooms until finely chopped. In a large, dry saucepan, cook mushrooms over medium heat until the moisture is gone and mushrooms are lightly browned, about 5 minutes.
Remove from heat and add shallots, green onions, parsley, thyme, salt, pepper, bread crumbs and canola oil. Mix well. Set this duxelle mixture aside.
In a lightly oiled 9x13 inch (22x33 cm) baking pan, spread crushed tomatoes. Stir in balsamic vinegar. Place fish fillets on top of tomatoes. Spoon duxelle mixture over fish, covering fillets.
Bake for 15-20 minutes until fish flakes easily with fork and mushroom mixture is lightly browned.