Heat 2 tablespoons olive oil in a large skillet over medium-high heat; cook onions until browned, tossing occasionally, 10 to 15 minutes. Season with salt and pepper; remove.
Heat remaining tablespoon oil in same skillet over high heat. Season steaks with salt and pepper. Cook 30 seconds on each side; remove. Add Worcestershire sauce and 2 tablespoons water to skillet, scraping up browned bits with a wooden spoon. Return onions to skillet; toss.
Sandwich steak and onions between toasted bread.