Heat oven to 425°F. Combine 2 tablespoons chives, horseradish and mustard in small bowl. Set aside.
Place mushrooms in mini food chopper container. Cover and process until finely ground.
Combine ground mushrooms and pepper, as desired, in small bowl; press evenly onto beef steaks. Heat 2 tablespoons oil in large nonstick skillet over medium-high heat. Place steaks in skillet; cook 4 to 6 minutes or until surface of beef is browned, turning once. Remove to a rimmed metal baking sheet. Season with salt, as desired. Keep warm.
Heat remaining 2 tablespoons oil in same skillet. Add bread crumbs; cook and stir 2 to 4 minutes or until crisp and golden brown. Remove from heat; stir in minced thyme.
Meanwhile spread horseradish mixture over tops of steaks. Top with bread crumbs, pressing gently to adhere. Roast in 425°F oven 9 to 13 minutes for medium rare to medium doneness. Tent loosely with aluminum foil. Let stand 4 minutes.
Sprinkle steaks with remaining 1 tablespoon chives. Garnish with thyme sprigs, if desired.