Take the steaks out of the refrigerator, pat them dry with paper towel and generously season with salt both sides and edges of them. Return to the refrigerator sitting in a dish with a rack, covered with aluminium foil.
An hour before using them take the steaks outside of the refrigerator and generously season with the pepper.
Set a large cast iron skillet or a heavy bottom non-stick saucepan over high heat and let it heat up for 2 minutes until smoking.
Lightly brush the steaks with 1 tablespoon of olive oil and carefully add the steaks in the skillet away from you, searing one side for 3 minutes. Flip the steaks and sear their other side for 3 more minutes.
Use an instant thermometer to check doneness aiming for 54 degrees C for medium doneness or 50 degrees C for medium-rare doneness.
Remove the steaks from the skillet and place on a pan with a rack and allow to rest, covered with foil, for 10 minutes before serving.
In the meantime, we should be make our red wine sauce. Put a small/medium deep saucepan over medium heat add the remaining 2 tablespoons of olive oil. Wait for a minute to heat a bit and add the shallots, sauté for 2-3 minutes while stirring continuously.
Add the garlic and the rosemary and sauté for 2 more minutes while stirring continuously.
Season with a pinch of black pepper and add the balsamic vinegar cooking for few minutes until it becomes thick and glossy at which time we add the wine and reduce to 1/3.
Reduce the heat to low, add the beef broth and simmer until reduced to half. Taste and if needed add some salt although the beef broth is usually quite salty, and you shouldn’t need to add more salt. Add the butter and whisk for 30 seconds and serve.