In a large skillet, heat oil over medium-high heat. Meanwhile, rinse trout; pat dry with paper towels. In a plastic bag, combine 1 tablespoon of the flour, 1/4 teaspoon salt, and 1/8 teaspoon pepper. Add fish to bag and shake to coat.
Place fillets in skillet, skin sides down. Cook fish for 3 minutes; turn fish and cook for 3 minutes more or until fish flakes easily with a fork. Transfer to a warm platter; keep warm.
In plastic bag, place remaining flour, 1/8 teaspoon salt and dash pepper. Add mushrooms and shake to lightly coat. In the same skillet, cook mushrooms and garlic in hot butter for 3 minutes or until browned and tender.
Add tomatoes and wine or broth; cook and stir until bubbly, loosening browned bits in skillet. Reduce heat and boil gently, uncovered, for 5 to 6 minutes or until sauce is slightly thickened (you should have about 1-3/4 cups). Add cooked asparagus; heat through. Serve sauce over fish. If you like, garnish with lemon wedges and fresh herb sprigs. Makes 2 to 4 servings.
For asparagus, cook in a small amount of boiling water for 4 to 6 minutes or until crisp-tender.