Sauté the mushrooms in the first amount given of butter and oil for about five minutes, or until lightly browned. Stir in the shallots and cook for a minute longer. Season the mushrooms and scrape them into a side dish.
Trim off the surrounding fat and filament from the beef and cut into 60g pieces, about 5cm across and 1cm thick. Dry thoroughly on paper towels.
Place butter and oil in the skillet and set over moderately high heat. When the butter foam begins to subside, sauté the beef, a few pieces at a time, for 2-3 minutes on each side to brown the exterior but keep the interior rosy red. Set the beef on a side dish and discard the fat.
Pour the wine and stock into the skillet and boil it down rapidly, scraping up the coagulated cooking juices, until liquid is reduced to about 1/3 cup. Beat in the cream, then the cornflour mixture. Simmer a minute. Add the mushrooms and simmer a minute more. The sauce should be lightly thickened. Correct seasonings.
Season the beef lightly with salt and pepper and return it to the skillet along with any juices which may have escaped. Baste the beef with the sauce and mushrooms, or transfer everything to a serving casserole.
When you are ready to serve, cover the skillet or casserole and heat to below the simmer for 3-4 minutes, being very careful not to overdo it or the pieces of filet will be well done rather than rare. Off heat and just before serving, tilt casserole, add butter to sauce a bit at a time while basting the meat until the butter has absorbed. Decorate with parsley and serve at once.