Preheat the oven to 400 degrees F. Be sure your stove is well ventilated!
Heat a large (10-inch) cast-iron skillet over high heat for 5 to 7 minutes. Pat the filets dry with paper towels and brush all over with the canola oil. Combine the fleur de sel and cracked pepper on a small plate and roll the filets on the top, bottom, and sides in the seasoning, pressing lightly to coat.
When the skillet is very hot, add the filets and sear evenly on all sides (top, bottom, and sides) for about 2 minutes per side.
Transfer the steaks from the skillet to a sheet pan (set the skillet aside) and place in the oven for 8 to 12 minutes, until the steaks register 120 degrees F on a meat thermometer for medium-rare. Remove from the oven, cover the pan tightly with aluminum foil, and allow to rest for 10 minutes.
Meanwhile, heat the butter in a medium (10-inch) saute pan over medium heat. Add the mushrooms and saute for 4 to 5 minutes, until they release their juices. Stir in the sherry and cook for 10 to 12 minutes, until the mushrooms are cooked through. Sprinkle with 1/2 teaspoon salt and 1/4 teaspoon pepper and set aside.
At the same time, add the olive oil to the skillet (don't wipe it out), add the shallots, and cook over medium heat for 2 minutes. Add the Cognac, stirring to deglaze the skillet, and cook for 2 minutes, until the Cognac evaporates and the shallots are tender. Stir in the cream and simmer for 4 to 5 minutes, until thickened. Stir in the two mustards and taste for seasonings.
Remove the strings from the filets and place on 4 warm dinner plates. Spoon the mustard sauce around the filets. Spoon the mushrooms on top of the filets and sprinkle each plate with parsley. Serve hot.
For taping this episode, Ina turned the heat off before adding the Cognac and then turned the heat on again. She also garnished each dinner plate with a small bunch of parsley instead of mincing the parsley.