Place steaks on plate. Press peppercorns and rosemary onto both sides.
Heat 2 tablespoons olive oil in heavy medium skillet over medium-high heat. Add garlic and 3/4 teaspoon rosemary and sauté 30 seconds. Add all mushrooms and sauté until beginning to soften, about 2 minutes. Add 1/2 tablespoon vinegar and stir to coat. Season mushrooms to taste with salt and pepper.
Meanwhile, heat 1 1/2 tablespoons oil in heavy large skillet over high heat. Sprinkle steaks with salt. Add to skillet and cook 2 minutes per side to brown. Reduce heat to medium-high and continue cooking until steaks are cooked to desired doneness, about 2 minutes per side for rare. Transfer to plates.
Add remaining 2 tablespoons vinegar and broth to skillet used for steaks; boil mixture until syrupy, scraping up browned bits, about 1 minute. Pour over steaks. Top with mushrooms and serve.