Heat oven to 350 degrees F.

Heat oil in a 12-inch nonstick ovenproof skillet over medium-high heat. Add onion and cook 4 minutes, until softened and beginning to brown. Add garlic and ginger; cook 30 seconds, until fragrant. Add mushrooms and 1 tablespoon of the sherry. Cover and cook 3 minutes, until softened. Stir mushrooms, and cook, uncovered, 5 minutes more, until mushrooms are lightly browned.

Meanwhile, whisk together chicken broth, teriyaki sauce, remaining 2 tablespoons sherry and cornstarch in a small bowl. Add to mushroom mixture and bring to a boil. Boil 30 seconds. Transfer to a bowl. Cover and keep warm.

Wipe out skillet. Sprinkle steak with salt and pepper. Heat the skillet over medium-high heat 2 minutes, until very hot. Add steak; cook 1-1/2 minutes per side, until browned. Transfer skillet to oven and bake steak 5 minutes. Remove skillet from oven, turn steak over and insert an instant-read meat thermometer on an angle into center of steak (temperature should register 140 degrees F for medium-rare). Transfer steak to a cutting board; let stand 5 minutes (temperature will increase to 145 degrees F). Slice steak; transfer to 4 serving plates and top with mushroom mixture. Makes 4 servings.