Pat the steaks dry on both sides with paper towels. Press each medallion with the palm of your hand to flatten it to about a 1-inch even thickness. Season all sides with the kosher salt and freshly cracked pepper. (Season the steaks right before cooking if you don’t have 60 minutes for them to sit at room temperature or to dry brine longer in the fridge.)

Heat a large, heavy-bottomed skillet over medium-high heat. Once hot, add one tablespoon of butter and one tablespoon of oil. Add the steaks and cook to the desired temperature, about 2 minutes per side for medium-rare (internal temperature of 130°F using a meat thermometer). Remove the steaks to a plate to rest and tent with foil.

Melt two tablespoons of butter with one tablespoon of olive oil over medium heat in the pan drippings. Increase the temperature to medium-high, add the mushrooms, and stir to coat them evenly with the butter and oil. Arrange them in a single layer, as best you can (they will shrink as they cook, allowing you to rearrange them). Cook the mushrooms for 3 minutes per side, or until golden brown. Remove the mushrooms from the skillet to a plate.

To the now-empty skillet, add two tablespoons of butter and melt over medium heat. Add the shallot and sauté for 3-4 minutes to soften. Add the tomato paste, garlic, and red pepper flakes and sauté for 30 seconds. (If using cognac, add 1/4 cup after sautéing and cook over medium-high heat to deglaze the pan.)

Add the flour and cook for 1 minute, scraping up the browned bits on the bottom of the pan. Reduce the heat to low and slowly whisk in the beef broth. Add the Worcestershire sauce, soy sauce, Dijon mustard, beef bouillon, oregano, and thyme. Bring to a simmer until thickened (it will thicken a little more with the cream). Stir in the heavy cream, parsley, and mushrooms, and warm through.

Plate the steaks with mashed potatoes and serve the sauce over the top, garnished with fresh parsley or chives. Season to taste (taste first!) with salt and pepper.