Heat the oil in a skillet over high heat. Sprinkle the fillets with salt and pepper on both sides. Place the fillets into the skillet and sear until golden brown. Turn the fillets over and continue cooking for 4 to 5 minutes for medium-rare doneness. Remove the fillets to a plate. Remove all but 1 1/2 tablespoons of the fat in the skillet and return to high heat. Add the mushrooms and shallots, and season with salt and pepper. Cook until golden brown and their liquid has evaporated. Add the red wine and cook until reduced by half. Add the stock and cook until reduced by half. Whisk in the butter and mustard and cook for 30 seconds. Taste and season with salt and pepper if needed. Garnish with the parsley.
Top the now-rested fillets with the sauce and taste.