Heat oven to 225 degrees F. Place fish on work surface. Season with 1/4 teaspoon salt and 1/4 teaspoon pepper. Dust with Wondra flour.
Heat large skillet over medium-high heat. Add 1 tablespoon oil, tilting pan to coat. Add fish; cook until golden, 2 minutes. Turn fillets over; cook until golden, 2 to 3 minutes. Transfer fish to baking dish.
Roast fish in 225 degree F oven until cooked through, 10 to 12 minutes.
Meanwhile, add remaining tablespoon oil to skillet. Reduce heat to medium. Add mushrooms. Season with remaining 1/4 teaspoon salt and pepper. Cook until softened, 5 minutes. Add shallot; cook 1 minute. Pour in wine; cook 2 minutes. Add broth; heat through. Stir in parsley and thyme. Remove from heat.
Divide mushroom mixture among 4 shallow bowls. Top with monkfish. Garnish with thyme, if desired. Makes 4 servings.