Bring filet mignon steaks to room temperature for about 30 minutes to 1 hour prior cooking to ensure the steak cooks quickly and evenly.
In a saucepan over medium-high heat, bring both the Madeira wine and the beef broth to a boil. Reduce the heat to medium and let simmer until only about half of the mixture (1-1/2 cup) remains and has slightly thickened. Reserve.
Use paper towels to pat the filet mignons dry, and then season the steaks on both sides with coarse salt and freshly ground black pepper. Reserve.
Meanwhile, heat a heavy-bottom large stainless steel or cast-iron skillet and add 1-1/2 tablespoon olive oil and 1 tablespoon butter. Over medium-high heat, sauté steaks until medium-rare (about 4 minutes per side). Transfer the steaks to a heated platter and cover loosely with foil while preparing the Madeira sauce.
Saute shallots and garlic in the skillet for about 1 minute. Add the previously reduced wine-stock mixture and the rosemary. Allow the mixture to bubble for 2 minutes, scraping up any browned bits. Remove from the heat and whisk in 2 tablespoons butter. When the butter has melted, return the steaks to the pan, turning them in the sauce. Serve!