Bring your steak to room temperature. Rub the steak with 1 tablespoon of extra virgin olive oil. Season with a pinch of sea salt, freshly ground black pepper, and smoked paprika.
Heat a cast-iron skillet or large pan over HIGH heat. Add the steak. Cook the steak for 2 minutes on each side until browned and cooked to medium rare. (see table above for cooking times)
Remove the pan from the heat and add the butter and sprig of rosemary to the pan. Spoon the butter over the steak.
Transfer the steak onto a cutting board and let it rest for 10 minutes.
Meanwhile, heat the remaining olive oil over LOW heat and crack the eggs into the pan. Cook the eggs for 3 minutes, or until set. Remove the eggs from the pan and season with salt and pepper.
Slice the steak into thick strips and serve with the eggs and other sides of your choice. Garnish with freshly chopped parsley and a pinch of smoked paprika.