Unlike muscley brisket, filet mignon comes from the tail end of the much smaller tenderloin. You won't have to do much (and shouldn't) to a filet mignon to get an almost buttery piece of meat.
Cooking beef tenderloin to the right temperature is crucial for achieving perfect doneness. For a rare roast, aim for an internal temperature of 120 to 125 F; for medium-rare, 130 to 135 F is ideal.