Season both sides of the filet mignon generously with salt and pepper. Wrap a piece of bacon around the sides of each steak and secure with butcher's twine. In a large heavy, ovenproof skillet, heat the olive oil over medium-high heat until almost smoking. Place the steaks in the hot pan and cook until well seared on 1 side, about 3 minutes. Turn the steaks over, there should be a nice crust on top. Add the mushrooms, garlic, and rosemary; give everything a good stir. Transfer the pan to the oven. Roast for 10 to 12 minutes or until the steaks are cooked medium-rare.
Remove the steaks, mushrooms, and rosemary to a platter; cover to keep warm. Return the pan to the stove over medium-high heat. Deglaze with the wine, scraping up all the yummy bits in the bottom of the pan. Mix in the demi-glace, stirring to combine. Put the steaks and mushrooms back in the pan and coat in the pan sauce. Finish with a couple of tablespoons of butter to make it rich. Put the steak and mushrooms on 2 serving plates and cut off the butcher's twine from the filets. Pour the wine sauce on top and garnish each plate with a roasted rosemary sprig.