Preheat the oven to 300F. Remove excess moisture from the beef, salt it and sprinkle with black pepper.
Melt the butter and start frying the beef - 4-5 minutes on each side. Add 2 sprigs of rosemary. It is convenient to turn the beef with large tongs.
Put the roast beef in a baking dish, pour in the broth and put 2 more sprigs of rosemary. Roast in oven for about 25 minutes depending on thickness (or about 15 minutes per pound of beef).
To achieve medium rare, the temperature inside the beef should be about 135 F. * remember that the temperature will rise another 5-10 degrees as it rests so remove once it's at 125 F or so ideally * 145 degrees F (for medium meat), or 150 degrees F (for medium well).
Cover and rest on the table for 15 minutes before slicing. If you want to serve this chilled, let cool, wrap in foil and refrigerate for 2 hours. Then unwrap and slice and serve.