Preheat the oven to 400 degrees F. Turn on your stove's fan for good ventilation.
Dry the filets well. Tie each filet with cooking string so they are all the same shape. Combine and mix two tablespoons of kosher salt and 2 teaspoons of coarsely ground black pepper on a plate. Lightly brush each filet with olive oil. Roll the filets in the salt and pepper mixture covering all sides, press to adhere the seasoning.
Heat a 10-inch cast-iron skillet over high heat for 5-7 minutes. When the skillet is hot, add the filets and sear them all over, about 2 minutes per side. Transfer the filets from the skillet to a baking sheet and place in the oven for 8-12 minutes or until the filets register 135 degrees F on a meat thermometer for medium rare. Remove from the oven, cover with foil and let rest for 10 minutes.
In the mean time, melt the butter in a medium sauté pan over medium heat. Add the shiitake mushrooms and sauté for about 5-7 minutes or until they have released their juices. Add the Sherry, stir to combine and simmer for about 10-12 minutes or until the mushrooms are tender. Season with salt and pepper.
At the same time using the cast-iron skillet from earlier (no need to wipe it out) , add the shallots and sauté over medium heat for about 2 minutes. Add the Cognac and cook for about 2 minutes, stirring to deglaze the skillet. When the Cognac has evaporated and the shallots are tender, stir in the heavy cream and simmer for about 5 minutes or until thickened. Stir in the mustards and adjust for seasoning.
To Serve: Remove the string from the filets. Place the filet on individual plates, spoon the mustard cream sauce around the filet and top with mushrooms. Garnish with parsley.