Season the Filet Mignon medallions with salt and pepper on both sides and rub them with a little olive oil.
On a hot skillet, over high heat, sear the meat on all sides. (2 minutes each side) They should be seared on the outside but still rare/medium rare on the inside. (Don’t worry, it will finish cooking in the sauce.) Reserve.
In that same skillet, add one Tablespoon of butter and sauté the mushrooms. Reserve with the Filet Mignon.
Using the same skillet again, add the 2 Tbsp of butter and, once it melts, add the flour and whisk it with the butter, making a roux. Cook the flour for a minute and add the beef broth and the Madeira wine. Whisk everything together until the sauce thickens. Season with salt and pepper and add back the Filet Mignon and the mushrooms.
Let the filet mignon cook in the sauce, turning them periodically, for a few minutes.
Plate the medallions with the mushrooms and the sauce on top.
Serve hot!