Heat 2 teaspoons oil in a medium saucepan over medium-high heat.
Add leeks, mushrooms, and garlic; cook, stirring constantly, 3 minutes.
Add water and rice; bring to a boil. Cover, reduce heat, and simmer 50 minutes or until rice is tender; drain. Stir in 1/2 teaspoon salt and black pepper. Set aside, and keep warm.
Combine flour and next 3 ingredients in a shallow dish; stir well. Dredge trout fillets in flour mixture.
Heat a large cast-iron skillet over medium- high heat until hot; add remaining 2 teaspoons oil.
Add fillets to skillet; cook in batches 2 minutes on each side or until fish flakes easily when tested with a fork.
Divide rice mixture evenly among 4 serving plates, and top each with 1 fillet.