Heat broiler.

Season the steak with 1/2 teaspoon salt and 1/2 teaspoon pepper. Line a rimmed baking sheet with foil. Place the steak on one half of the baking sheet.

Toss the tomatoes and onion in a medium bowl with the oil, vinegar, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Place the onion and tomatoes, cut-side down, on the other half of the baking sheet.

Broil the steak and vegetables, turning everything once, until the steak reaches the desired doneness, 4 minutes per side for medium rare. Remove the steak and return the vegetables to oven until browned, about 1 minute more.

Slice the steak. Place the bottom halves of the bread cut-side up and top with the steak, onions, tomatoes, and cheese. Sandwich with the remaining bread. Serve warm.

Substitution: If blue cheese is too strong for your taste, try topping this sandwich with a creamy goat cheese. Or play off the tartness of the balsamic vinegar with slivers of salty Parmesan or Manchego.