Sprinkle the steaks liberally with salt and pepper.
Heat the oil over medium-high heat in a large cast-iron skillet or other skillet that is already hot.
Add the steaks and sear for 3 to 5 minutes per side (longer if you like your steak well-done).
Remove the steaks to a clean large plate and allow them to rest while you make the sauce.
Reduce the heat to medium and add the shallots and a few teaspoons of the beef stock to the skillet. Scrape up any of the browned bits left by the steaks.
Add the tomatoes and cook for about 1 minute to slightly soften them.
Add the remaining stock, arugula and balsamic vinegar and cook just until the arugula is wilted.
Arrange the steaks on plates, place the tomatoes and arugula all around, spoon on the sauce and serve at once.