Translated literally, this phrase means “delicate fillet” or “cute fillet.” I can’t say I’ve ever thought of a steak as cute, but I guess if you’re gonna use that label, this is the cut that deserves it.
(I have a vague memory of a literary character or maybe a literary character’s pet being named Mignon, but the details are escaping me. It wasn’t Goethe, which seems to be all that Google will dredge up.)
Back to food. If you order this in France, you won’t get beef; you’ll get pork, though it will still be the tenderloin portion. (To get the beef version there you’d ask for “tournedo,” which you have likely seen on some fancy menu here in the backwoods. How did this disconnect occur? It’s unclear, but it seems that the generally accepted answer was that beef was simply more prevalent in the U.S., and chefs were trying to move product so they started using the label for the wrong animal.
Sort of like the Royale with Cheese, the name is incidental. This stuff rocks.
That said, I don’t know the first thing about making it taste good, so I consulted the expert, and here’s what he had to say:
When my lovely bride asked me to write a 250-word treatise on how to grill a good filet mignon, I told her I could do it in three.
Buy good steak.
But I couldn’t get away with that. It’s necessary, but not sufficient, I was told.
So here’s what I can tell you.
Buy good steak.
If you can avoid it, don’t freeze it. But if you have to freeze it, it’s not a huge deal. Just thaw it in the fridge then get it close to room temperature before you grill.
Some people don’t season their steaks. That’s OK. I don’t like sauces. I argue that a good steak doesn’t need a sauce. It’s just as valid to argue that a good steak doesn’t need seasoning.
But if you do season …
Season the steak a few hours before you’re ready to grill. That will enhance the flavor.
Seasoning, like pizza, is largely a matter of personal taste. I use Lawry’s seasoned salt, pepper, and onion powder. Your mileage may vary.
Use charcoal. It’s better than gas. And don’t spread the charcoal all the way across. Leave at least a third of the grill plate uncovered.
Let the charcoal get white hot. Put the steaks directly above the charcoal. Close the lid.
How long to cook depends on how you like your steak and how thick it is.
So, figure that timing out, and allow for about half that time to be spent off the direct heat.
I’m a medium-well guy, so I’ll cook a fairly thick filet for about seven minutes on one side, turn it, another seven minutes, then I’ll move it off the direct heat and turn it one more time. This can take anywhere from 6-10 minutes, again depending on how you like your steak and the thickness. If you like ‘em rare, it might not need any indirect heat at all.

I don’t cook steaks often, because my bride prefers hers to look like a charred black chunk of mess (Well done is like medium rare to her). We also can’t order steak in a restaurant, because no chef really understands why someone would burn the hell out of something that tastes so good. But, like your extremely smart husband, I also use charcoal only, no matter what I’m cooking. It’s how I grew up, and if it was good enough for my granny, then it’s the smart way to cook.