Combine the dried oregano, red pepper flakes, bay leaf and 1 tablespoon salt in a coffee or spice grinder and pulse until finely ground. Rub evenly over both sides of the steaks. Set aside to marinate at room temperature for 15 minutes.
Meanwhile, put the potatoes in a heavy-bottomed saucepan with enough cold water to cover by 1/2 inch. Salt the water generously, bring to a simmer and cook, covered, until the potatoes are fork tender, about 10 minutes. Drain, return to the pot with 3 tablespoons of the butter and mash with a fork or potato masher. Stir in the mustard and 1/4 cup of the chicken broth until creamy. Season with salt.
Heat a large skillet over medium-high heat. When hot, add 2 tablespoons of the oil. Cook the steaks until crusty and browned on one side, about 4 minutes. Flip and cook, adding the remaining 1 tablespoon oil if needed, until browned on the other side, about 3 minutes more for medium-rare. Remove the steaks and set aside to rest.
Add the mushrooms to the skillet and cook until browned, about 3 minutes. Add the red wine and the remaining 1/2 cup chicken broth and cook until reduced by half, about 5 minutes. Swirl in the remaining 3 tablespoons butter until the sauce is glossy and thick.
Transfer the steaks to a serving plate and transfer the potatoes to a serving bowl. Spoon the sauce over the steaks and top with fresh oregano. Serve with the potatoes.