For this recipe, be sure to use good-quality sweet and tart dried apricots, like Blenheims; they make a wonderful accent to the sesame-crusted fish. Slideshow: More Quick Fish Recipes
Spread the sesame seeds on a plate. Rub the trout fillets with 2 tablespoons of the canola oil and season with salt and pepper. Coat the flesh side of each fillet with sesame seeds, pressing gently to help them adhere.
Preheat the broiler. In a nonstick skillet, heat 2 tablespoons of the canola oil. Place 2 fillets skin side down in the skillet and cook over moderate heat until the skin is crisp and the fish is almost cooked through, 5 minutes. Transfer the fillets skin side down to a rack set over a baking sheet. Wipe out the skillet and cook the remaining 2 fillets in the remaining 2 tablespoons of canola oil. Broil 8 inches from the heat until the seeds are golden and the fish is cooked through, 3 minutes. Transfer to plates.
Melt the butter in the skillet. Add the shallots and garlic; cook over moderate heat, stirring, until the butter is golden brown, about 3 minutes. Off the heat, stir in the preserves, dried apricots, lemon juice, sesame oil and parsley. Season with salt and pepper, spoon over the fish and serve with lemon wedges.
Dry Riesling from Alsace tends to have stone fruit flavors that are ideal with this dish.